UPSC CDS 2 2021 Math Paper

Concept:The angle subtended by a chord at the center of a circle is twice the angle subtended by it at any point on the remaining circumference.Explanation:$AB$ is a diameter of the circle with center $O$.Chord $BP$ subtends $\angle BOP$ at the center $O$ and $\angle BAP$ at point $A$ on the circumference.By the central angle theorem, we have: $\angle BOP = 2 \times \angle BAP$.From the given figure or problem context, $\angle BOP = 90^{\circ}$.Therefore, $\angle BAP = \frac{1}{2} \times \angle BOP = \frac{1}{2} \times 90^{\circ} = 45^{\circ}$.Thus, the required angle is $45^{\circ}$.Answer:$\angle BAP = 45^{\circ}$ (Option C).