SSC CGL 23 Aug 2021 Shift 2 Paper

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Question : 52 of 100

Marks: +1, -0

A tangent is drawn from a point

P

to a circle, which meets the circle at

T

such that

P T=8 {cm}

. A secant

P A B

intersects the circle in points

A

A

and

B

. If

P A=5 {cm}

, what is the length (in

{cm}

) of the chord

A B

?

$8.0$
$8.4$
$6.4$
$7.8$

Solution:

Given,

P T=8 {cm}, P A=5 {cm}

We know that,

(P T)^{2}=P B × P A

⇒ \;\; (8)^{2}=P B × 5

⇒ \;\; \;{64}/{5}=P B

⇒ \;\; P B=10.8 {cm}

∴

Length of chord

A B=P B-A P

=12.8-5

B=7.8 {cm}

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