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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 the value of PRD?


  1. 60

  2. 50

  3. 20

  4. Can't be determined 


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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