Circle Question 9
Question 9 - 2024 (31 Jan Shift 1)
If one of the diameters of the circle $x^{2}+y^{2}-10 x+4 y+13=0$ is a chord of another circle $C$, whose center is the point of intersection of the lines $2 x+3 y=12$ and $3 x-2 y=5$, then the radius of the circle $\mathrm{C}$ is
(1) $\sqrt{20}$
(2) 4
(3) 6
(4) $3 \sqrt{2}$
Show Answer
Answer (3)
Solution
$2 x+3 y=12$
$3 x-2 y=5$
$13 x=39$
$x=3, y=2$
Center of given circle is $(5,-2)$
Radius $\sqrt{25+4-13}=4$
$\therefore C M=\sqrt{4+16}=5 \sqrt{2}$
$\therefore C P=\sqrt{16+20}=6$
