Solve any four sub-questions:

In the following figure, a tangent segment PA touching a circle in A and a secant PBC are shown. If AP = 15, Bp = 10, find BC.

The diagram is as follows:

Given,

Ray PA ia tangent and PBC is a secant.

AP = 15 cm

BP = 10 cm

We Know that by Tangent Secant Theorem,

According to tangent-secant theorem:

“When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment.”

Mathematically,

(Tangent)² = (Whole Secant) × (External Secant)

PA² = PB × PC ……………. (By Tangent Secant Property)

15² = 10 × PC

PC × 10 = 225

PC = 22.5cm

Now we have calculated the total length of secant PC.

So PB + BC = PC

10 + BC = 22.5

∴ BC = 12.5 cm