Question

The triangle $PQR$ is inscribed in the circle, $x^2+y^2=20$. If $Q$ and $R$ have co-ordinates $(3,4)$ & $(-4,3)$ 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 $\frac{\pi }{4}$

We know the radius of circumcircle

$R=\frac{a}{2\sin A}{x}^2+y^2=5^2\Rightarrow R=5QR=\sqrt{(3+4{)}^2+(4-3{)}^2}QR=\sqrt{7^2+1^2}=\sqrt{50}=5\sqrt{2}5=\frac{5\sqrt{2}}{2\sin P}\sin P=\frac{1}{\sqrt{2}}\angle P=\frac{\pi }{4}\angle QPR=\frac{\pi }{4}$