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Given A circle with centre O and an external point T and two tangents TP and TQ to the circle, where P, Q are the points of contact.
To Prove: {tex}\angle{/tex}PTQ = 2{tex}\angle{/tex}OPQ
Proof: Let {tex}\angle{/tex}PTQ = {tex}\theta{/tex}
Since TP, TQ are tangents drawn from point T to the circle.
TP = TQ
{tex}\therefore{/tex} TPQ is an isoscles triangle
{tex}\therefore{/tex} {tex}\angle{/tex}TPQ = {tex}\angle{/tex}TQP = {tex}\frac12{/tex} (180^o - {tex}\theta{/tex}) = 90^o - {tex}\fracθ2{/tex}
Since, TP is a tangent to the circle at point of contact P
{tex}\therefore{/tex} {tex}\angle{/tex}OPT = 90^o
{tex}\therefore{/tex} {tex}\angle{/tex}OPQ = {tex}\angle{/tex}OPT - {tex}\angle{/tex}TPQ = 90^o - (90^o - {tex}\frac12{/tex} {tex}\theta{/tex}) = {tex}\fracθ2{/tex}= {tex}\frac12{/tex}{tex}\angle{/tex}PTQ
Thus, {tex}\angle{/tex}PTQ = 2{tex}\angle{/tex}OPQ

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7/75 is terminating or non - terminating

Posted by Vaibhav Pandey 7 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Anuj Bansal 7 years, 9 months ago

Non terminating

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Is there anyother word which can be used at the place of outcomes in math in question paper?

Posted by Me Bhawna 7 years, 9 months ago

CBSE > Class 10 > Mathematics

2 answers

Me Bhawna 7 years, 9 months ago

Thanks shivani

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Harshita Vatyani 7 years, 9 months ago

Outcome is only proper word

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If x=30° then verify that Tan2x=2tanx

Posted by Himanshu Pal 7 years, 9 months ago

CBSE > Class 10 > Mathematics

4 answers

Harry Sood 7 years, 9 months ago

Question for not exist.

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Anuj Bansal 7 years, 9 months ago

Impossible

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Keshav Bindal 7 years, 9 months ago

No tan2x is no equal to 2tanx

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Ritu Dhingra 7 years, 9 months ago

Its wrong..tan2x is mot equal to 2tanx

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If a,b and c are the sides of an right angle triangle , where c is the hypotenus then prove that the radius of its inCircle is equal a+b+c/2

Posted by Akshat Kacholia 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let a,b and c be the sides of right angled {tex} \triangle ABC{/tex}, such that BC = a, CA = b and AB = c.
Let the circle touches the sides BC, CA, AB at D, E and F, respectively.

Then, {tex}AE=AF{/tex}
and {tex}BD=BF{/tex}
and {tex}CD=CE{/tex} [tangents drawn from an external point are equal in length]
In quadrilateral OECD each angle is right angle .So, OECD is a square therefore, we have
{tex}OE=EC=CD=OD=r{/tex}
{tex}\therefore AF=AE=b-r\;{/tex} and {tex}BF=BD=a-r{/tex}
{tex}\Rightarrow AF+BF=(b-r)+(a-r){/tex}
{tex}\Rightarrow AB=b-r+a-r{/tex}
{tex}\Rightarrow c=a+b-2r{/tex}
{tex}\Rightarrow\ 2r=a+b-c{/tex}
{tex}\therefore r=\frac{a+b-c}{2}{/tex}

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The difference between two number is 26 and one number is three times the other . Find them..........................

Posted by Shakshi Singh 7 years, 9 months ago

CBSE > Class 10 > Mathematics

2 answers

Harshita Vatyani 7 years, 9 months ago

13&39

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Divya Darshni 7 years, 9 months ago

Let the two numbers be x and y difference between them is 26 therefore, x - y = 26 ---(1) One number is three times the other therefore x = 3y Sub x in equation (1) 3y - y = 26 2y = 26 y = 26/2 = 13 X = 3y = 3 (13) = 39 Thereforevthe two numbers are 39 and 13

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The area of three face of rectangular block are in the ratio 2:3:4 and volume 9 000 . find length of shortest side.

Posted by Sourav Choudhary 7 years, 9 months ago

CBSE > Class 10 > Mathematics