In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2. ST is…

GATE · 2025 · EE · General Aptitude

In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2.

ST is parallel to QR. Two semicircles are drawn with PS and PQ as diameters, as shown in the figure.

Which one of the following statements is true about the shaded area PQS?

Note: The figure shown is representative.

1. A.

   The shaded area is $\frac{16}{9}$ times the area of the semicircle with the diameter PS.

2. B.

   The shaded area is equal to the area of the semicircle with the diameter PS.

3. C.

   The shaded area is $\frac{14}{9}$ times the area of the semicircle with the diameter PS.

4. D.

   The shaded area is $\frac{14}{25}$ times the area of the semicircle with the diameter PQ.

Attempted by 3 students.