Question

From the diagram below, if AC is a tangent line, and if PD = 9 and DC = 32, find the length of BC.

Answer 1

Solution:

Given the circle;

From the circle theorem, triangle PBC is a right triangle.

$\begin{gathered} PB=PD=9 \\ \\ PC=PD+DC=9+32 \\ \\ PC=41 \end{gathered}$

Using the Pythagorean theorem;

$\begin{gathered} BC=\sqrt{PC^2-PB^2} \\ \\ BC=\sqrt{41^2-9^2} \\ \\ BC=\sqrt{1600} \\ \\ BC=40 \end{gathered}$

CORRECT OPTION: C