Question

Use the following information to find PD and EQ.

Answer 1

Answer:

$PD = 18$

$EQ = 4$

Step-by-step 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

$\frac{36}{2} = PD$

$18 = PD$

$PD = 18$

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

$EQ = \frac{56}{14}$

$EQ = 4$