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Mathematics

PQ is a tangent to a circle at point P. Centre of the circle is O. If ΔOPQ is an isosceles triangle, then ∠QOP =

  1. 30°

  2. 60°

  3. 45°

  4. 90°

Circles

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Answer

PQ is a tangent to a circle at point P. Centre of the circle is O. If ΔOPQ is an isosceles triangle, then ∠QOP. Tangent Properties of Circles, RSA Mathematics Solutions ICSE Class 10.

Let QP = OP

We know that,

The tangent at any point of a circle and the radius through this point are perpendicular to each other.

∠OPQ = 90°

∠QOP = ∠OQP = x [Anglers opposite to equal sides are equal in a triangle]

By angles sum triangle property,

x + x + 90° = 180°

2x + 90° = 180°

2x = 180° - 90°

2x = 90°

x = 90°2\dfrac{90°}{2}

x = 45°

∠QOP = 45°

Hence, option 3 is the correct option.

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