Question

\(RP\) and \(RQ\) are the two tangents to the circle with centre \(O\) and \(∠POQ=110°\), then \(∠PRQ=\) _____ .

• A. 70°
• B. 90°
• C. 35°
• D. 100°

Answer 1

The Correct Option is A

To solve the problem, we need to find the angle \( \angle PRQ \) formed between the two tangents drawn from a point outside the circle.

1. Geometry of Tangents from External Point:
When two tangents are drawn from an external point to a circle, the triangle formed (in this case \( \triangle PRQ \)) is isosceles and angle between the tangents at the circle’s center \( \angle POQ \) is given.

2. Use the Property of Triangle:
The triangle \( \triangle POQ \) formed at the center by joining the tangents' points of contact has the angle \( \angle POQ = 110^\circ \).
Now, the angle between the tangents at the external point \( \angle PRQ \) is the external angle for triangle \( \triangle POQ \):

\[ \angle PRQ = 180^\circ - \angle POQ = 180^\circ - 110^\circ = 70^\circ \]

Final Answer:
The value of \( \angle PRQ \) is \( 70^\circ \).