Question

The triangle $PQR$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$ then $\angle QPR=$

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

Answer 1

Answer: (A), (C)

The correct options are
A $\frac{\pi }{4}$
C $\frac{3\pi }{4}$

Circle $\Rightarrow x^2+y^2=25$

Center is $0(0,0)$

$Q=(3,4)$

$R=(-4,3)$

$\angle QOR={90}^o$ or ${270}^o$

So $\angle QPR=\frac{\angle QOR}{2}$

$={45}^o$ or $1350$.