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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 C

20°


ADB is a straight line

ADP + PDB = 180

100 + PDB = 180

PDB = 80

Similarly QED = 80

∠DPE = 90 (angle subtended by a diameter)

∠PED = 10 (DPE + PED + EDP = 180)

Similarly QDE = 10

∠DRE = 160 (DRE + RDE + RED = 180)

PRE is a straight line

PRD + DRE = 180

PRD + 160 = 180

PRD = 20


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