Triangle PQR is inscribed in circle {x^2} + {y^2} = 25 . If Q and R have co-ordinates (3,4) and (-4,

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9.Straight Line

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

A

$\frac{\pi }{2}$

B

$\frac{\pi }{3}$

C

$\frac{\pi }{4}$

D

$\frac{\pi }{6}$

(IIT-2000)

Solution

(c) Here the centre $0\,(0,0)$. So ‘$m$’ of $OQ$ is $\frac{4}{3}$and ‘$m$’ of $OR$ is $\frac{{ – 3}}{4}$, $\angle QOR = \frac{\pi }{2}$

Hence $\angle QPR = \frac{1}{2} \times \frac{\pi }{2} = \frac{\pi }{4}$.

Standard 11

Mathematics

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