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Question

If PQ = RS and ORS=48 in the given figure, what are the values of OPQ and SOR?


A
84, 48
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B
48, 84
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C
38, 68
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D
78, 84
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Solution

The correct option is B 48, 84
Consider the ORS.
Note that OR = OS = radius of the circle. Since the angles opposite to equal sides are equal, we have ORS=OSR=48.
But, using angle sum property
ORS+RSO+SOR=180.

i.e., 48+48+SOR=180
SOR=18096=84
Now, since equal chords subtend equal angles at the centre and since PQ=RS,
SOR=POQ=84.
It can be noted that OPQ is also isosceles.
OPQ=OQP
Thus, using angle sum property in OPQ,
OPQ=180842=48.

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