Question

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

Answer 1

Here, PC is a secant and AP is a tangent.
By secant tangent theorem, we have:
$$\begin{gathered} \mathrm{PB}\times \mathrm{PC}={\mathrm{AP}}^2 \\ \Rightarrow 10\times \mathrm{PC}={15}^2 \\ \Rightarrow \mathrm{PC}=\frac{225}{10}=22.5\mathrm{units} \\ \therefore \mathrm{BC}=\mathrm{PC}-\mathrm{PB}=22.5-10=12.5\mathrm{units} \end{gathered}$$