CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

To show that the perimeter of AABL is constant, we need to prove that AB + BA + AL + BL is constant.

First, let us label the angles in the figure as follows:

∠NLM = ∠LNM = α (since LM and LN are tangents from an external point, they are equal in measure)
∠MAB = β (angle between the tangent AB and the chord MC)
∠NBA = β (angle between the tangent AB and the chord NC)
∠ALN = γ (angle between the tangent LN and the chord MN)
∠BLM = γ (angle between the tangent LM and the chord MN)

Using the fact that the sum of angles in a triangle is 180 degrees, we can write:

∠LAM = 180 - α - β
∠LBN = 180 - α - β

Now, let us consider the perimeter of AABL:

AB + BA + AL + BL

Using the fact that angles in the same segment of a circle are equal, we can write:

∠MCN = ∠MAB + ∠NBA = 2β

Using the fact that the opposite angles in a cyclic quadrilateral add up to 180 degrees, we can write:

∠ALB = 180 - ∠MCN = 180 - 2β

Now, let us consider the triangles LAM and LBN. Using the fact that angles in a triangle add up to 180 degrees, we can write:

∠LAM + ∠ALN + ∠ALM = 180
∠LBN + ∠BLM + ∠BLN = 180

Substituting the values we have calculated for ∠LAM and ∠LBN, and using the fact that ∠ALN = ∠BLM = γ, we get:

(180 - α - β) + γ + ∠ALM = 180
(180 - α - β) + γ + ∠BLN = 180

Simplifying, we get:

∠ALM = α + β - γ
∠BLN = α + β - γ

Finally, let us consider the perimeter of AABL again:

AB + BA + AL + BL = AB + BA + 2AL sin γ + 2BL sin γ

Using the fact that AL = AM and BL = BN, and using the sine rule in triangles LAM and LBN, we get:

AB + BA + 2AM sin γ + 2BN sin γ = AB + BA + 2LM sin (α + β - γ) + 2LN sin (α + β - γ)

Using the fact that LM = LN (since they are tangents from an external point), we get:

AB + BA + 2LM sin (α + β - γ) + 2LM sin (α + β - γ)

Simplifying, we get:

AB + BA + 4LM sin (α + β - γ)

Using the fact that sin (α + β - γ) = sin (180 - γ) = sin γ, we get:

AB + BA + 4LM sin γ

Substituting the value of LM (which is equal to LN), we get:

AB + BA + 4LN sin γ

But we know that sin γ is a constant, since it is determined by the position of point L and the circle MN. Therefore, the perimeter of AABL is constant, since it does not depend on the position of point C on the arc MN.

Hence, we have proved that the perimeter of AABL is constant.

0Thank You

ANSWER

What is fundamental theorem of arthmetics?

Posted by Umang Upadhyay 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Arshad Alam 2 years ago

Every composite number can be expanded in the product of prime no. Such tha p and q

0Thank You

Aman Baghel 2 years ago

Every composite number can be written in the product of prime no.

0Thank You

Ashish Ojha 2 years ago

This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

Few rules to keep homework help section safe, clean and informative.

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

1Thank You

ANSWER

If X=2sin^2A and Y = 2cos^2A +1 then the value of X+Y =

Posted by Arvind Kumar 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Ashish Ojha 2 years ago

0Thank You

Nitish Yadav 2 years ago

Answer is 3

1Thank You

ANSWER

Check weather 301is a term of the list of numbers 5,11,17,23....

Posted by Ashish Raj 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Omya Aryan 2 years ago

No, since n=50.3

0Thank You

Riya Lama 2 years ago

2Thank You

Ashish Raj 2 years ago

n- 67

4Thank You

ANSWER

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Gotum Sevak Sevak 2 years ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Math basic blueprint

Posted by Anushka Gusain 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Riya Lama 2 years ago

Send karte hu

0Thank You

Riya Lama 2 years ago

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

0Thank You

ANSWER

some blueprint for math standard plz?

Posted by Wellz Sari 2 years ago

CBSE > Class 10 > Mathematics

1 answers

Shandilya Gupta 2 years ago

I also need it

0Thank You

ANSWER

Two different dice are tossed together. Find the probability (1) that the number on each die is even. (2) that the sum of numbers appearing on the two dice is 5.

Posted by Itz__Kritika Koli 🖤 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Tanvi Verma 2 years ago

1.) 1/4 2.) 1/9

0Thank You

Ankit Class 2 years ago

(2) 1/9

0Thank You

Ankit Class 2 years ago

(1 ) 1/4

0Thank You

ANSWER

Solve for x. 1/x + 1/2p + 1/2q = 1/x +2p +2q

Posted by Madhu Paswan 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Madhu Paswan 2 years ago

x=-2p x=-2q

1Thank You

Madhu Paswan 2 years ago

x=-2p x=-2q

0Thank You

ANSWER

BPT AAYGI KYA

Posted by Siddharth Choudhary 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Soniya Pandey 2 years ago

Imp h bhut

1Thank You

Wellz Sari 2 years ago

ha aur bahat imp hai

1Thank You

Naman Singh Rawat 2 years ago

Yes

1Thank You

ANSWER

Is it compulsory to show whole process of MCQ in boards?

Posted by Khushi Patel 2 years ago

CBSE > Class 10 > Mathematics

5 answers

Wellz Sari 2 years ago

0Thank You

Shanu Yadav 2 years ago

Noo

0Thank You

Srishti Thakur 2 years ago

No you have to only write the correct options of mcqs

0Thank You

Itz__Kritika Koli 🖤 2 years ago

That means no..

1Thank You

Itz__Kritika Koli 🖤 2 years ago

Step by step solution is not required in MCQ type questions. Only tick/write down the correct option. Writing a complete solution is nothing but wastage of time in board.

0Thank You

ANSWER

The nth term of the AP a,3a, 5a... is (a) na (b) (2n-1)a (c) (2n+1)a (d) 2na

Posted by Rounak Gupta 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Omya Aryan 2 years ago

Nth term = a+(n-1)d… a+(n-1)2a… a+2an-2a… 2an-a… (2n-1)a… option (b)

0Thank You

Itz__Kritika Koli 🖤 2 years ago

Option no. (b) (2n-1)a

0Thank You

ANSWER

(6q+1)(6q+2)(6q+3)

Posted by Nothing Nothing 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Preeti Dabral 2 years ago

(6q+1)(6q+2)(6q+3)

in all 6q is common

then 6q is out

=6q(1+2+3)

=6q(6)

=36q/6

=6q

Yes, this is divisible by 6.

0Thank You

_Jass_ Mahey_ 2 years ago

0Thank You

ANSWER

Let k be a positive integer , if 5 divides k² , then 5 also divides

Posted by Krishna Gupta 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Itz__Kritika Koli 🖤 2 years ago

If 5 divides k² then 5 also divides K

0Thank You

Karan Raj 2 years ago

0Thank You

ANSWER

Kon sa chapter sbse important h math m...plz.tell me ...i am hindi medium.student so plz tell me.in hindi..

Posted by Abhi® Rana 2 years ago

CBSE > Class 10 > Mathematics

1 answers

Omya Aryan 2 years ago

Trigonometry

0Thank You

ANSWER

Oh that any positive or integer is of the form 4q + 1 or 4q + 3 where q is some integer

Posted by Khushi Khushi 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Omya Aryan 2 years ago

Not in syllabus

0Thank You

Itz__Kritika Koli 🖤 2 years ago

By Euclid's division algorithm, a=bq+r Take b=4 Since 0 < r < 4, r = 0,1,2,3 So, a=4q,4q+1,4q+2,4q+3 Clearly, a=4q,4q+2 are even, as they are divisible by 2. Therefore 'a' cannot be 4q,4q+2 as a is odd. But 4q+1,4q+3 are odd, as they are not divisible by 2. Any positive odd integer is of the form (4q+1) or (4q+3).

0Thank You

Abhi® Rana 2 years ago

Hlo....HINDI...M PUCHO TO BTA SKTE H.

0Thank You

ANSWER

The sum of the probability of all the elementary events of an experiment is____

Posted by Pardeep Sharma 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Shanu Yadav 2 years ago

0Thank You

Adarsh Singh Adarsh Singh 2 years ago

0Thank You

ANSWER

substitute method maths 7x-15y=2 x+2y=3

Posted by Suyash Salunkhe 2 years ago

CBSE > Class 10 > Mathematics

1 answers

Shristi Kumari 2 years ago

7×-15y=2 eq 1 ×+2y=3 eq 2 From eq 1 7×=2+15y ×=2+15y apon 7 Answer

0Thank You

ANSWER

lesson no 3

Posted by Suyash Salunkhe 2 years ago

CBSE > Class 10 > Mathematics

2 answers

_Jass_ Mahey_ 2 years ago

Pair linear equations in two variables

0Thank You

Karan Raj 2 years ago

Pair of linear equation

0Thank You

ANSWER

Find the sum of 25 terms of an AP in which d=5 and the 11th term is 55.

Posted by Prithvi Sharma 2 years ago

CBSE > Class 10 > Mathematics

2 answers

Bhavuk Kataria 2 years ago

125

0Thank You

Prithvi Sharma 2 years ago

2Thank You

ANSWER

if theta is an acute angle and cosec thetha = root 5.Find.the value of cot theta minus cos thetha

Posted by Prince Kesharwani 2 years ago

CBSE > Class 10 > Mathematics

1 answers

Ankit Class 2 years ago

Let theta be angle A Cosec A =√5 Cot A- cos A CosA/sinA -cosA CosA(cosecA-1) SinA = 1/√5 CosA =√1-sin^2 A CosA= √ 1-1/5 CosA=√4/5 CosA=2/√5 Now CotA-cosA=cosA(cosecA-1) CotA-cosA=2/√5(√5-1)

0Thank You

ANSWER

Use euclids division algorithm to find HCF of 504 and 980

Posted by Abhijai Utsav 2 years ago

CBSE > Class 10 > Mathematics

1 answers

🥱🥱 ... 2 years ago

ye deleted h...

1Thank You

ANSWER

What is the value of cos 30

Posted by Bittu Yadav 2 years ago

CBSE > Class 10 > Mathematics

5 answers

Itz__Kritika Koli 🖤 2 years ago

√3/2

0Thank You

Harshita Saini 2 years ago

Root 3 / 2

0Thank You

Angel Shibu Angel Shibu 2 years ago

√ 3/2

0Thank You

Omya Aryan 2 years ago

√3/2

0Thank You

Jatin Kaushik 2 years ago

1÷√3

0Thank You

ANSWER

Prove that parellelgram circumscribing a circle is a rhombus

Posted by Kavita Hiremath 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Hardik Kamble 2 years ago

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

0Thank You

Karan Kundar 2 years ago

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

1Thank You

Pawan Gambhir 2 years ago

Ncert question

0Thank You

ANSWER

4/x + 9/x+10 = 1/2

Posted by Kavita Hiremath 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Itz__Kritika Koli 🖤 2 years ago

4/x + 9/x + 10 = 1/2 20x + 26 = x 20x + 26 - 26 = x - 26 20x = x-26 20x-x=x-26-x 19x=x-26-x 19x=-26 19x/19=26/19 x=-26/19 Answer...

0Thank You

Pooja Kumari 2 years ago

-26/19

0Thank You

Ankush Pahwa 2 years ago

LHS TAKING LCM x WE GET,, 4+9+10x/x =1/2 13+10x/x =1/2 CROSS MULTIPLICATION LHS & RHS WE GET,,, 26+20x = x 26= x-20x 26= -19x x = 26/-19 ANSWER

2Thank You

ANSWER

+-equal to

Posted by Laksh Chauhan 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Itz__Kritika Koli 🖤 2 years ago

+ - is equal to -

0Thank You

Harshita Saini 2 years ago

0Thank You

Abhi® Rana 2 years ago

Hlo .....guys ...best of luck 21 march matmatic exam and plz bless me....HAR HAR MHADEV ............AGAR KISI KO BHEE BAAT KRNE H TO MUJE CALL KR SKTA H OR HM SATH M MATH K EXAMPLE .SOLUTION ETC KRENGE ....NUMBER TBHI MILEGA JN REPLY M KOI MESSAGE AAYEGA ......THANKU...💜

4Thank You

ANSWER

x2+(y-3V2x)2=1

Posted by Ananya Kumari 2 years ago

CBSE > Class 10 > Mathematics

1 answers

Aditi Chaudhary 2 years ago

x2+(y-3V2x)2=1 is a equation of an ellipse in the coordinates plane. The equation of an ellipse is typically given in a form of (x^2)/a^2+(y^2)/b^2 = 1, where a and b are the lengths of a semi major and semi minar axes, respectively. In the given equation , the semi major axis is 1 and semi minar axis is sqrt(3)

3Thank You

ANSWER

Cosec A - Sin A / Sec A- Cos A = 1/ tan A + cot A

Posted by Sriram Surendiran 2 years ago

CBSE > Class 10 > Mathematics