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Question

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ADP = BEQ = 100. What is value of PRD?

 



A

60

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B

50

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C

20

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D

Can't be determined 

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Solution

The correct option is D

20


ADB is a straight line. By linear pair axiom,
ADP + PDB = 180
100 + PDB = 180
PDB = 80
Similarly QED = 80

We have, ∠DPE = 90 (angle subtended by a diameter)

In DPE,
DPE + PED + EDP = 180
[Angle sum property of a triangle]
∠PED = 10 
Similarly QDE = 10

In DRE,
DRE + RDE + RED = 180
[Angle sum property of a triangle]
∠DRE = 160

PRE is a straight line. By linear pair axiom,
PRD + DRE = 180
PRD + 160 = 180
PRD = 20


Mathematics

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