Question

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

• A. $\pi /2$
  
• B. $\pi /3$
  
• C. $\pi /4$
  
• D. $\pi /6$
  

Answer 1

Answer: (C)

Let $O$ is the point at centre and $P$ is the point at circumference. Therefore, angle $QOR$ is double the angle $QPR$. So, it is sufficient to find the angle $QOR$.

Now, slope of $OQ,m_1=4/3$,
slope of $OR,m_2=-3/4$
Here, $m_1{m}_2=-1$
Therefore, $\angle QOR=\pi /2$
which implies that $\angle QPR=\pi /4$