Question

If a circle C, whose radius is 3, touches externally the circle, $x^2+y^2+2x–4y–4=0$ at the point $(2,2)$, then the length of the intercept cut by this circle C, on the $X$-axis is equal to :

• A.
  $2\sqrt{3}$
• B. $\sqrt{5}$
• C. $3\sqrt{2}$
• D. $2\sqrt{5}$

Answer 1

The correct option is D $2\sqrt{5}$

centre of the given circle$=(-1,2)$
and radius = $3$
By section formula:
Centre of the required circle=$(5,2)$
Radius =$3$
So required circle C is $x^2+y^2-10x-4y+20=0$
length of $X$ intercept$=2\sqrt{g^2-c}=2\sqrt{5}$