Question

From the diagram below, if AC is a tangent line, and if PD = 3 and DC = 2, find the length of BC.

Answer 1

Explanation

From the diagram

$\begin{gathered} radius\text{ of cicle =}PB=PD=3 \\ PC=PD+DC=3+2=5 \end{gathered}$

Therefore;

$\begin{gathered} PC^2=PB^2+BC^2 \\ 5^2=3^2+BC^2 \\ 25=9+BC^2 \\ BC^2=25-9 \\ BC^2=16 \\ BC=\sqrt{16} \\ BC=4 \end{gathered}$

Answer: Option A