First slide

Definition of a circle

Question

The $Δ P Q R$ is inscribed in the circle $x^{2} + y^{2} = 25$ . If $Q$ and $R$ have coordinates $(3, 4)$ and $(- 4, 3)$ respectively, then $∠ Q P R$ is equal to

Moderate

A

$\frac{π}{2}$
B

$\frac{π}{3}$
C

$\frac{π}{4}$
D

$\frac{π}{6}$

Solution

Ans:3
$L e t m_{1} = s l o p e$
$o f O Q = \frac{4}{3} a n d m_{2} = s l o p e$
$o f O R = \frac{- 3}{4} . A s m_{1} m_{2} = - 1, R (- 4, 3)$
$∠ Q O R = \frac{π}{2}$
$T h u s, ∠ Q O R = \frac{π}{4}$
$(\begin{matrix} ∵ a n g l e s u b t e n d e d a t t h e c e n t r e o f a c i r c l e i s d o u b l e d \\ t h e a n g l e s u b t e n d e d in t h e a l t e r n a t e s e g m e n t \end{matrix})$

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