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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. 1:1

  2. 3:1

  3. 4:1

  4. 2:1


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, OQPORP  [RHS congruency]
Hence, OPQ=OPR  [CPCT]

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