The triangle PQR is inscribed in the circle x | vedclass

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(C) The circle is given by $x^2 + y^2 = 25$,which has its center at the origin $O(0, 0)$ and radius $r = 5$.The coordinates of $Q$ are $(3, 4)$ and $R

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$\frac{\pi}{4}$

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(C) The circle is given by $x^2 + y^2 = 25$,which has its center at the origin $O(0, 0)$ and radius $r = 5$.The coordinates of $Q$ are $(3, 4)$ and $R$ are $(-4, 3)$.The slope of $OQ$ is $m_1 = \frac{4 - 0}{3 - 0} = \frac{4}{3}$.The slope of $OR$ is $m_2 = \frac{3 - 0}{-4 - 0} = -\frac{3}{4}$.Since $m_1 	imes m_2 = \left(\frac{4}{3}ight) 	imes \left(-\frac{3}{4}ight) = -1$,the lines $OQ$ and $OR$ are perpendicular to each other.Therefore,the central angle $\angle QOR = \frac{\pi}{2}$.According to the circle theorem,the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.Thus,$\angle QPR = \frac{1}{2} \angle QOR = \frac{1}{2} 	imes \frac{\pi}{2} = \frac{\pi}{4}$.

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

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