In the circle below, if the segments PD = 3, DB = 5, and PC = 2, find segment CA.

Question

asked Jan 17, 2023 232k views

1 Answer

Alexandre Bell · Answer 1 · 2023-01-22T05:08:40+0000

Given,

PD = 3, DB = 5, and PC = 2

Required

The value of segment CA.

By the definition of secant of the circle.

$\begin{gathered} (AC+CP)* CP=(BD+DP)* DP \\ (AC+2)*2=(5+3)*3 \\ (AC+2)=8*(3)/(2) \\ AC=4*3-2 \\ AC=10 \end{gathered}$

Hence, the measure of segment AC is 10.