Question

Use the following information to find PD and EQ.

AP = 3, PQ = 5, QB = 7, CP=2, and QD = 14
Find PD and EQ

Answer 1

`PD = 18`

`EQ = 4`

Explanation:

Given:

AP = 3,

PQ = 5,

QB = 7,

CP = 2,

QD = 14

Required:

1. PD

2. EQ

SOLUTION:

1. Based on Intersecting Chords Theorem,

`AP*PB = CP*PD`

AP = 3

PB = PQ + QB = 5 + 7 = 12

CP = 2

PD = ?

Plug in the values into the equation

`3*12 = 2*PD`

`36 = 2*PD`

Divide both sides by 2

`(36)/(2) = PD`

`18 = PD`

`PD = 18`

b. Based on Intersecting Chords Theorem,

`EQ*QD = AQ*QB`

EQ = ?

QD = 14

AQ = AP + PQ = 3 + 5 = 8

QB = 7

Plug in the values into the equation

`EQ*14 = 8*7`

`EQ*14 = 56`

Divide both sides by 14

`EQ = (56)/(14)`

`EQ = 4`