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Question

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:
 
  1. 2:1
  2. 3:1
  3. 4:1
  4. 1:1


Solution

The correct option is D 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,
ΔOQPΔORP (RHS congruency)
Hence,
OPQ=OPR(CPCT)
So,
OPROPQ=11

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