UPSC CDS 2 2021 Math Paper

Given,
AB is a diameter of a circle with centre O.
Radius OP is perpendicular to AB and Q is any point on arcPB.
Since, chord PB makes ∠BOP at the centre and ∠BAP at A.∴∠BAP=‌

1

2

∠BOP
[since, angle made by a chord at a point present on the circle is half of the angle made by chord on the centre]
∠BAP=‌

1

2

×90∘=45∘
Hence, ∠BAP is equal to 45∘.