PQ is tangent to a circle with centre O. If ...

CBSE Class 10 Standard Math 2026 All Sets Solved Paper

Question : 8 of 20

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PQ is tangent to a circle with centre O. If ∠POR = 65°, then m∠OPR is

Solution:

In ∆ POR,

OP = OR (radii).

Therefore, ∠OPR = ∠ORP (angles opposite to equal sides).

The sum of angles in a triangle is 180°.

In ∆ POR

∠POR + ∠OPR + ∠ORP = 180°

65° + x + x = 180°

65° + 2x = 180°

2x = 180° − 65°

2x = 115°

x = \;\frac{115^{\circ}}{2} = 57.5^{\circ}

So, m∠OPR = 57.5°

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