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

ValenceElectron asked Jan 20, 2023

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ValenceElectron asked Jan 20, 2023

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15 votes

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;

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

CORRECT OPTION: C

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