Question

In the given circle, PA is tangent and PBC is secant, PA = 8 cm and PB = 4 cm. The length of BC is:

Options

• 8 cm

• 12 cm

• 16 cm

• 2 cm

Answer 1

12 cm

Explanation: 

We know that,

If a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.

⇒ PB × PC = PA²

⇒ 4 × PC = 8²

⇒ 4 × PC = 64

⇒ PC = `64/4`​ = 16 cm.

From figure,

BC = PC − PB = 16 − 4 = 12 cm.