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GATE 2026 PI – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

PQ is a diameter of the circle centered at O. R,S lie on the circle and ∠ROS = 80°. PR and QS extended meet at T as shown. Find ∠RTS.

Diagram for GATE 2026 PI question 7
  1. 40°
  2. 50°
  3. 60°
  4. 80°

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Show answer and explanation

Correct answer: (B) 50°

Explanation

The angle between two secants meeting outside a circle equals half the difference of their intercepted arcs. The diameter intercepts $180^\circ$ and the inner arc RS is $80^\circ$. Therefore $\angle RTS=(180^\circ-80^\circ)/2=50^\circ$: **B**.

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