Question
Download Solution PDFLet 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Centre of the circle, O
External point, P
PQ and PR are tangents to the circle at Q and R respectively
∠ROQ = 110°
Formula Used:
∠PQR = 90° and ∠PRQ = 90° (radius of a circle and a tangent line are always perpendicular to each other)
Sum of all angles of Quadrilateral = 360°
Calculation:
∠ROQ = 110°
Using the formula:
∠ROQ + ∠PQR + ∠PRQ + ∠RPQ = 360°
⇒ 110° + 90° + 90° +∠RPQ = 360°
⇒ ∠RPQ = 360° - 290°
⇒ ∠RPQ = 70°
The correct answer is option 3: 70°
Last updated on Jun 26, 2025
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