GATE Electrical 2025 | GA | Question: 10

Question

In the triangle $P Q R$, the lengths of $P T$ and $T R$ 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.

• A. The shaded area is $\frac{16}{9}$ times the area of the semicircle with the diameter PS.
• B. The shaded area is equal to the area of the semicircle with the diameter PS.
• C. The shaded area is $\frac{14}{9}$ times the area of the semicircle with the diameter PS.
• D. The shaded area is $\frac{14}{25}$ times the area of the semicircle with the diameter PQ.

Comments

option $A$ seems correct.