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Question

PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then
OPR:OPQ =.

A
2:1
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B
1:1
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C
1:2
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D
4:1
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Solution

The correct option is B 1:1

Join the points OP, OQ and OR.
In OPQ and OPR,OP=OP (common side) OQ=OR (radii of the same circle)OQP=ORP=90(Tangent is perpendicular to the radius)ΔOQPΔORP (RHS congruency)

Hence, OPQ=OPR (CPCT)
OPROPQ=11OPR:OPQ=1:1

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