SATHEE: Circle 2 Question 10

Circle 2 Question 10

11. The $△ P Q R$ 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

$(2000, 2 M)$

(a) $π / 2$

(b) $π / 3$

(d) $π / 6$

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Answer:

Correct Answer: 11. (a)

Solution:

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, $∠ Q O R = π / 2$

which implies that $∠ Q P R = π / 4$

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Circle 2 Question 10

11. The △PQR is inscribed in the circle x2+y2=25. If Q and R have coordinates (3,4) and (−4,3) respectively, then ∠QPR is equal to

Answer:

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11. The $△ P Q R$ 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