NDA 2 2024 Maths, question 62

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.

Q62

What are the coordinates of $A$ ?

(a) $(-6,8)$
(b) $(-6,-8)$
(c) $(5\sqrt{2},5\sqrt{2})$
(d) Cannot be determined due to insufficient dataCorrect answer

Solution.

Answer: (d) Cannot be determined due to insufficient data

The shared data specify B,C and the circle but do not locate A on it.
Infinitely many points on the circle, excluding B and C, form such a triangle.
The angle relation does not select one point, so A cannot be uniquely determined.