NDA 2 2024 Maths, question 61

Topic: Analytical geometry

Passage · Q61 to Q62

A triangle $ABC$ is inscribed in the circle $x^{2}+y^{2}=100$ . $B$ and $C$ have coordinates $(6,8)$ and $(-8,6)$ respectively.

Q61

What is $\angle BAC$ equal to?

(a) $\pi/2$
(b) $\pi/3\text{ or }2\pi/3$
(c) $\pi/4\text{ or }3\pi/4$ Correct answer
(d) $\pi/6\text{ or }5\pi/6$

Solution.

Answer: (c) $\pi/4\text{ or }3\pi/4$

OB·OC=6(−8)+8(6)=0, so the smaller central angle BOC is 90°.
An angle at the circumference subtending BC is half either intercepted arc, giving 45° or 135°, namely π/4 or 3π/4, depending on A's arc.