Answer:
[tex] PD = 18 [/tex]
[tex] EQ = 4 [/tex]
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,
[tex] AP*PB = CP*PD [/tex]
AP = 3
PB = PQ + QB = 5 + 7 = 12
CP = 2
PD = ?
Plug in the values into the equation
[tex] 3*12 = 2*PD [/tex]
[tex] 36 = 2*PD [/tex]
Divide both sides by 2
[tex] \frac{36}{2} = PD [/tex]
[tex] 18 = PD [/tex]
[tex] PD = 18 [/tex]
b. Based on Intersecting Chords Theorem,
[tex] EQ*QD = AQ*QB [/tex]
EQ = ?
QD = 14
AQ = AP + PQ = 3 + 5 = 8
QB = 7
Plug in the values into the equation
[tex] EQ*14 = 8*7 [/tex]
[tex] EQ*14 = 56 [/tex]
Divide both sides by 14
[tex] EQ = \frac{56}{14} [/tex]
[tex] EQ = 4 [/tex]
