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Question

In figure if PQR is tangent to circle at Q whose centre is O. AB is a chord parallel to PR and BQR=70 then AQB is equal to
291810_d709134b86a449269636db8933196363.png

A
20
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B
40
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C
35
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D
45
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Solution

The correct option is C 40
PQR is a tangent. Thus, OQR=90(Angle between tangent and radius)
Thus, OQB=90BQR
OQB=20
Let the line from O meet AB at M. Now In MQA and MQB
QMA=QMB (Each 90, as ABPR)
QM=QM (common)
MA=MB (Perpendicular from centre bisects the chord)
Thus, QMAQMB (SAS rule)
Hence, MQA=MQB=20
Hence, AQB=40

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