PQR is an equilateral triangle inscribed in a circle S is any point on the arc QR Find the mea...........

Quantitative Aptitude (CGL) Geometry

? PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Find the measure of ∠ PSQ.

This questions was previously asked in

Combined Graduate Level Examination Tier I 2023

30^°

60^°

90^°

45^°

- In an equilateral triangle inscribed in a circle, all sides and angles are equal. For triangle PQR, each angle is 60°.

- The key property of a circle is that any angle subtended by the same arc at the circle's center is twice any angle subtended at the circumference.

- Arc QR subtends angle ?QSR at the center and at any point like S on the circle.

- Since PQR is equilateral, angle PQS and angle PRS are each 60°.

- Due to the property of the circumcircle, angle ?PSQ is half of angle ?PQR, which makes ?PSQ = 60°.

Correct Answer: Option 2, 60°

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