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

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$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{6}$

answer is C.

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Detailed Solution

$x^{2} + y^{2} = 25 C = (0, 0) r = 5 Q (3, 4), R (- 4, 3) slope of C Q = \frac{4}{3} slope of CR = \frac{- 3}{4} C Q ⊥ CR \Rightarrow ∠ Q C R = \frac{π}{2} N o w L Q PR = \frac{π}{4}$

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