Question
Download Solution PDFIn the figure given below, O is the centre of the circle. If ∠APQ = 35°, find the value of ∠OQP.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFAccording to the alternate segment theorem, the angle between a tangent and a chord at the point of contact is equal to the angle made by the chord in the alternate segment of the circle
In the figure given,
⇒ ∠APQ = ∠QRP = 35°
As we know, the angle subtended by an arc at the centre of the circle is twice the angle subtended by the arc at any other point on the circle
⇒ ∠QOP = 2 × ∠QRP = 2 × 35° = 70°
Now, considering ΔOQP,
∵ OQ = OP = radius of circle
⇒ ΔOQP is an isosceles triangle
⇒ ∠OQP = ∠OPQ
∵ Sum of angles of triangle = 180°
⇒ ∠QOP + ∠OQP + ∠OPQ = 180°
∴ ∠OQP = (180° – 70°)/2 = 110°/2 = 55°
Last updated on Jul 22, 2025
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