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.

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ANSWER

What is fundamental theorem of arthmetics?

Posted by Umang Upadhyay 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Arshad Alam 1 year, 8 months ago

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

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Aman Baghel 1 year, 8 months ago

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

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Ashish Ojha 1 year, 8 months ago

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

Posted by Arvind Kumar 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Ashish Ojha 1 year, 8 months ago

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Nitish Yadav 1 year, 8 months ago

Answer is 3

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

Posted by Ashish Raj 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Omya Aryan 1 year, 8 months ago

No, since n=50.3

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Riya Lama 1 year, 8 months ago

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Ashish Raj 1 year, 8 months ago

n- 67

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Posted by Gotum Sevak Sevak 1 year, 8 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Math basic blueprint

Posted by Anushka Gusain 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Riya Lama 1 year, 8 months ago

Send karte hu

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Riya Lama 1 year, 8 months ago

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some blueprint for math standard plz?

Posted by Wellz Sari 1 year, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Shandilya Gupta 1 year, 8 months ago

I also need it

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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 🖤 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Tanvi Verma 1 year, 8 months ago

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

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Ankit Class 1 year, 8 months ago

(2) 1/9

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Ankit Class 1 year, 8 months ago

(1 ) 1/4

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

Posted by Madhu Paswan 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Madhu Paswan 1 year, 8 months ago

x=-2p x=-2q

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Madhu Paswan 1 year, 8 months ago

x=-2p x=-2q

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BPT AAYGI KYA

Posted by Siddharth Choudhary 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Soniya Pandey 1 year, 8 months ago

Imp h bhut

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Wellz Sari 1 year, 8 months ago

ha aur bahat imp hai

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Naman Singh Rawat 1 year, 8 months ago

Yes

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

Posted by Khushi Patel 1 year, 8 months ago

CBSE > Class 10 > Mathematics

5 answers

Wellz Sari 1 year, 8 months ago

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Shanu Yadav 1 year, 8 months ago

Noo

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Srishti Thakur 1 year, 8 months ago

No you have to only write the correct options of mcqs

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Itz__Kritika Koli 🖤 1 year, 8 months ago

That means no..

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Itz__Kritika Koli 🖤 1 year, 8 months 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.

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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 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Omya Aryan 1 year, 8 months ago

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

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Itz__Kritika Koli 🖤 1 year, 8 months ago

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

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

Posted by Nothing Nothing 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Preeti Dabral 1 year, 8 months 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.

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_Jass_ Mahey_ 1 year, 7 months ago

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

Posted by Krishna Gupta 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Itz__Kritika Koli 🖤 1 year, 8 months ago

If 5 divides k² then 5 also divides K

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Karan Raj 1 year, 8 months ago

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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 1 year, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Omya Aryan 1 year, 8 months ago

Trigonometry

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

Posted by Khushi Khushi 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Omya Aryan 1 year, 8 months ago

Not in syllabus

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Itz__Kritika Koli 🖤 1 year, 8 months 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).

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Abhi® Rana 1 year, 8 months ago

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

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

Posted by Pardeep Sharma 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Shanu Yadav 1 year, 8 months ago

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Adarsh Singh Adarsh Singh 1 year, 8 months ago

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

Posted by Suyash Salunkhe 1 year, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Shristi Kumari 1 year, 8 months ago

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

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lesson no 3

Posted by Suyash Salunkhe 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

_Jass_ Mahey_ 1 year, 7 months ago

Pair linear equations in two variables

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Karan Raj 1 year, 8 months ago

Pair of linear equation

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

Posted by Prithvi Sharma 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Bhavuk Kataria 1 year, 8 months ago

125

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Prithvi Sharma 1 year, 8 months ago

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

Posted by Prince Kesharwani 1 year, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Ankit Class 1 year, 8 months 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)

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Use euclids division algorithm to find HCF of 504 and 980

Posted by Abhijai Utsav 1 year, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

🥱🥱 ... 1 year, 8 months ago

ye deleted h...

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What is the value of cos 30

Posted by Bittu Yadav 1 year, 8 months ago

CBSE > Class 10 > Mathematics

5 answers

Itz__Kritika Koli 🖤 1 year, 8 months ago

√3/2

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Harshita Saini 1 year, 8 months ago

Root 3 / 2

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Angel Shibu Angel Shibu 1 year, 8 months ago

√ 3/2

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Omya Aryan 1 year, 8 months ago

√3/2

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Jatin Kaushik 1 year, 8 months ago

1÷√3

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Prove that parellelgram circumscribing a circle is a rhombus

Posted by Kavita Hiremath 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Hardik Kamble 1 year, 8 months 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.
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Karan Kundar 1 year, 8 months ago

Don't post personal information, mobile numbers and other details.
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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.
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Pawan Gambhir 1 year, 8 months ago

Ncert question

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

Posted by Kavita Hiremath 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Itz__Kritika Koli 🖤 1 year, 8 months 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...

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Pooja Kumari 1 year, 8 months ago

-26/19

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Ankush Pahwa 1 year, 8 months 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

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+-equal to

Posted by Laksh Chauhan 1 year, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Itz__Kritika Koli 🖤 1 year, 8 months ago

+ - is equal to -

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Harshita Saini 1 year, 8 months ago

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Abhi® Rana 1 year, 8 months 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...💜

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x2+(y-3V2x)2=1

Posted by Ananya Kumari 1 year, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Aditi Chaudhary 1 year, 8 months 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)

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

Posted by Sriram Surendiran 1 year, 8 months ago

CBSE > Class 10 > Mathematics