GATE 2026 EE – Question 7
In the given figure, $\overline{PQ}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle ROS=80^\circ$. When $\overline{PR}$ and $\overline{QS}$ are extended, they meet at $T$. The value of $\angle RTS$ is ________________.
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Correct answer: (B) 50°
Explanation
$T$ is outside the circle, where two secants meet. The angle between them is half the difference of the intercepted arcs: the far arc $PQ$ (a semicircle, $180^\circ$) and the near arc $RS$ ($80^\circ$). So $\angle RTS=\tfrac12(180^\circ-80^\circ)=50^\circ$.