A triangle PQR is inscribed in the circle x^2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The circle is $x^2 + y^2 = 5^2$,with center $O(0, 0)$ and radius $r = 5$.Let $Q = (3, 4)$ and $R = (-4, 3)$.The slope of $OQ$ is $m_1 = \frac{4-0}

Vedclass · Accepted Answer

$\pi /4$

Vedclass · Answer

(C) The circle is $x^2 + y^2 = 5^2$,with center $O(0, 0)$ and radius $r = 5$.Let $Q = (3, 4)$ and $R = (-4, 3)$.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 $m_1 	imes m_2 = \frac{4}{3} 	imes (-\frac{3}{4}) = -1$,the lines $OQ$ and $OR$ are perpendicular.Thus,the central angle $\angle QOR = \frac{\pi}{2}$.By 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.Therefore,$\angle QPR = \frac{1}{2} \angle QOR = \frac{1}{2} 	imes \frac{\pi}{2} = \frac{\pi}{4}$.

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

Similar Questions

Let the centre of the circle $S=0$ lie on the line $x+y-5=0$ and also lie in the first quadrant. If this circle touches both the lines $x-2=0$ and $y-5=0$,then the area of the circle is

For the line $3x + 2y = 12$ and the circle $x^2 + y^2 - 4x - 6y + 3 = 0$,which of the following statements is true?

Does the point $(-2.5, 3.5)$ lie inside,outside,or on the circle $x^{2}+y^{2}=25$?

Given three collinear points $A(3,1)$,$B(7,-1)$,and $C(5,0)$. The length of a tangent drawn from $A$ to any circle that passes through $B$ and $C$ is ....... units.

If a circle passes through the points $(0,0), (x,0),$ and $(0,y)$,then the coordinates of its centre are

Vedclass Test Series

Exam Paper Generator

Online Exam Module