From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is:
A
1:1
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B
2:1
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C
3:1
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D
4:1
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Solution
The correct option is A 1:1 Join the points OP,OQ and OR Now, in triangles OPQ and OPR, OP = OP (common side) OQ = OR (radii) ∠OQP=∠ORP=90∘ (Tangent is perpendicular to the radius) Hence, ΔOQP≅ΔORP (RHS congruency) Hence, ∠OPQ=∠OPR(CPCT) So, ∠OPR∠OPQ=11