Question

The triangle PQR is inscribed in the circle $x^2+y^2=25$ such that P lies on the major arc QR. If Q and R have coordinates $(3,4)$ and $(-4,3)$ respectively, then $\angle QPR$ is equal to

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{6}$

Answer 1

The correct option is C $\frac{\pi }{4}$

Slope of OQ = $\frac{4}{3}$
Slope of OR =$-\frac{3}{4}$
$\therefore \angle ROQ={90}^{\circ }$

The central angle is twice the angle inscribed in the arc.
$\therefore \angle QPR=\frac{\pi }{4}$