The triangle P Q R is inscribed in the circle x 2 + y 2 = 25 . If Q and R have co-ordinates (3, 4) and ( - 4 , 3 ) respectively, then Q P R is equal to [2000]

Question

The triangle $P Q R$ is inscribed in the circle $x^{2} + y^{2} = 25$ . If $Q$ and $R$ have co-ordinates (3, 4) and $(- 4, 3)$ respectively, then $∠ Q P R$ is equal to [2000]

Smart Achievers · Accepted Answer

(3)

$O$ is the point at centre and $P$ is the point at circumference. Therefore, angle QOR is double the angle QPR.

So, it is sufficient to find the angle QOR. Now slope of $O Q = \frac{4}{3} = m_{1} (let)$

Slope of $O R = - \frac{3}{4} = m_{2} (let); Now, m_{1} m_{2} = - 1$

$Therefore, ∠ Q O R = 90 °$ $∴$ $∠ Q P R = 45 ° .$

Solution

Q.
The triangle $P Q R$ is inscribed in the circle $x^{2} + y^{2} = 25$ . If $Q$ and $R$ have co-ordinates (3, 4) and $(- 4, 3)$ respectively, then $∠ Q P R$ is equal to [2000]

1 $\frac{π}{2}$

2 $\frac{π}{3}$

3 $\frac{π}{4}$

4 $\frac{π}{6}$

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Solution

Q. The triangle PQR is inscribed in the circle x2+y2=25. If Q and R have co-ordinates (3, 4) and (-4,3) respectively, then ∠QPR is equal to [2000]

1 π2

2 π3

3 π4

4 π6