Question

PLEASE HELP I'M DESPERATE

Examine the following diagram, where AP is secant to the circle at points A and B, and CP is secant to the circle at points C and D. The lines intersect outside the circle at point P. What is the length of PD?

11

7

12

9

Answer 1

Explanation:

The formula for 2 secants coming out of a common point is a proportion

The formula in this case, is

PA*PB = CD * PC

Givens

PB = 10

PA = 8 + 10 = 18

PD = X

PC = X + 20

Solution

10*18 = x * (x + 20) Cross Multiply

180 = x^2 + 20x Remove the Brackets

180 -180 = x^2 + 20x -180 Subtract 180 from both sides.

0 = x^2 +20x - 180 Combine

This factors into something not in your answer choices or even close rounded.

Make sure you have the right diagram for the right question.