Chord AB of a circle with radius 5 cm is at a distance of…

Chord AB of a circle with radius 5 cm is at a distance of 4 cm from the centre O. If tangents drawn at A and B intersect at P, then find the length of the tangent AP.

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 3.75 cm

Given:

Radius = 5cm

Distance of chord from center = 4 cm

Explanation:

According to the given question,

Let the perpendicular bisects chord at X, then

In triangle XOA, (OA)² = (OX)² + (AX)²

⇒ (AX)²= 25 - 16

⇒ (AX)²= 9

⇒ AX = 3

Also, triangles OAX and APX are similar

⇒ ${OA \over OX} = {AP \over AX}$

⇒ ${5 \over 4} = {AP \over 3}$

⇒ AP = $15 \over 4$ = 3.75

Hence the required answer is 3.75 cm.

SSC CHSL 2021 PYQ — Question 72