Question

# In the adjoining figure, If $$O$$ is the center of the circle and the angle $$x=y$$,  then which of the following is true?

A
2OA=RA
B
OA=PA
C
PQ=RS
D
RO=RS

Solution

## The correct option is A $$PQ = RS$$From the above figure $$RS=RA+AS$$ and $$PQ=PA+QA$$$$\Delta RDA$$ and $$\Delta ADP$$ are congruence triangle Hence $$RA=AP$$ now in $$\Delta AQM$$ and $$\Delta ASM$$     $$\angle QAM=\angle SAM$$Hence $$\Delta AQM$$ and $$\Delta ASM$$ are congruence triangle Hence $$AQ=AS$$ Hence $$RS=PQ$$Mathematics

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