111k views
0 votes
In the diagram below, segment PB is a tangent. IF AC = 12 and PA = 4, find PB.

In the diagram below, segment PB is a tangent. IF AC = 12 and PA = 4, find PB.-example-1

1 Answer

2 votes

We would apply the tangent secant theorem which states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment. From the diagram,

tangent segment = PB

secant segment = PC

external secant segment = PA

By applying the theorem,

PA x PC = PB^2

From the information given,

AC = 12

PA = 4

PC = AC + PA = 12 + 4 = 16

Thus,

4 x 16 = PB^2

PB^2 = 64

PB = √64

PB = 8

User David Gee
by
4.0k points