If one of the diameters of the circle x^2+y^2-10 x+4 y+13=0 is a chord of another circle […

Question

If one of the diameters of the circle $x^2+y^2-10 x+4 y+13=0$ is a chord of another circle $$\mathrm{C}$$, whose center is the point of intersection of the lines $2 x+3 y=12$ and $3 x-2 y=5$

Accepted Answer

$$\begin{aligned}
& 2 x+3 y=12 \
& 3 x-2 y=5
\end{aligned}$$

$$\begin{aligned}
& 13 x=39 \
& x=3, y=2
\end{aligned}$$

Center of given circle is $(5,-2)$

Radius $$\sqrt{25+4-13}=4$$

$$\begin{aligned}
& \therefore \mathrm{CM}=\sqrt{4+16}=5 \sqrt{2} \
& \therefore \mathrm{CP}=\sqrt{16+20}=6
\end{aligned}$$

Solutions · 1