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CBSE Class 10 Basic Math 2026 All Sets Solved Paper

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Question : 15 of 20
Marks: +1, -0
In the given figure, PQ and PR are two tangents drawn to a circle with centre O. If ∠ORQ = 25°, then the measure of ∠PQR is:
Solution:  
Given: PQ and PR are tangents to the circle with centre O.
∠ORQ = 25°
In In ∆ ORQ
OR = OQ (Radii of the same circle)
∠OQR = ∠ORQ (Angles opposite to equal sides are equal)
∠OQR = 25°
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
OQ ⟂ PQ
∠OQP = 90°
From the figure:
∠PQR = ∠OQP − ∠OQR
∠PQR = 90° − 25°
∠PQR = 65°
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