Question

The radius of the circle with centre at $\left(3,2\right)$ and whose common chord with the circle $C:x^{2}+y^{2}-4x-8y+16=0$ is also a diameter of the circle $C$ , is

• A. $3$ units
• B. $2$ units
• C. $1$ unit
• D. $\sqrt{3}$ units

Answer 1

Answer: (A)

Let the equation of the circle be $x^{2}+y^{2}-6x-4y+c=0$
So, the common chord of these $2$ circles is
$2x-4y+16-c=0$
It passes through the centre $\left(2,4\right)$ of the given circle, so
$4-16+16-c=0\Rightarrow c=4$
Hence, the radius of the circle $=\sqrt{9 + 4 - 4}=3$ units