Question

In the given figure,PQ and PR are two tangents to a circle with centre O. if <QPR = 46° then calculate <QOR​

Answer 1

Given PQ and PR are the two tangents drawn from a point P to a circle with center point O & ∠QPR =46°

We know that the tangent to a circle makes an angle 90° with the radius of the circle.

so, PQOR forms a Quadrilateral  with ∠PQO = ∠PRO = 90°  & ∠QPR = 46°

We know sum of the angles of quadrilateral = 360°

⇒ ∠PQO + ∠PRO + ∠QPR + ∠QOR = 360°

⇒ 90° + 90° + 46° + ∠QOR = 360°

⇒ ∠QOR = 360° - 90° - 90° - 46°

         ∠QOR = 134°.

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