Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$m_1=$ slope of OP = $\frac{4}{3}$ and $m_2$ slope of $OQ=\frac{-3}{4}\Rightarrow m_1{m}_2=-1$ (Where O is the origin) ,$\angle QOP=\frac{\pi }{2}$
Thus $\angle QPR=\frac{\pi }{4}$