Circle 2 Question 10

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

$(2000,2 M)$

(a) $\pi / 2$

(b) $\pi / 3$

(c) $\pi / 4$

(d) $\pi / 6$

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Answer:

Correct Answer: 11. (a)

Solution:

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

Now, slope of $O Q, m _1=4 / 3$,

slope of $O R, m _2=-3 / 4$

Here,

$m _1 m _2=-1$

Therefore, $\quad \angle Q O R=\pi / 2$

which implies that $\angle Q P R=\pi / 4$



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