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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?
375607.bmp


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