Let C be a circle with Centre O and P be an external point to C. Let PQ and PR be the tangents to C such that Q and R be the points of tangency, respectively. If ∠ROQ = 110°, find ∠RPQ.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 70°.
The sum of all angles of Quadrilateral = 360°
So
∠ROQ + ∠PQR + ∠PRQ + ∠RPQ = 360°
⇒ 110° + 90° + 90° +∠RPQ = 360° (∠PQR = 90° and ∠PRQ = 90° (radius of a circle and a tangent line are always perpendicular to each other))
⇒ ∠RPQ = 360° - 290°
⇒ ∠RPQ = 70°