The equation of incircle of the triangle formed by common tangents to the circles x2+y2=4 and x2+y2-6x+8=0 is

Question

The equation of incircle of the triangle formed by common tangents to the circles x2+y2=4 and x2+y2-6x+8=0 is (A) x2+y2=1 (B) x2+y2-6x+8=0 (C) x2+y2-6x+9=0 (D) x2-y2=1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-x6cw7dpqoqnr.png" /> Note that circles touch each other externally, hence the smaller circle is incircle of the triangle formed by common tangents.

Q. The equation of incircle of the triangle formed by common tangents to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} - 6 x + 8 = 0$ is

$x^{2} + y^{2} = 1$

$x^{2} + y^{2} - 6 x + 8 = 0$

$x^{2} + y^{2} - 6 x + 9 = 0$

$x^{2} - y^{2} = 1$

Note that circles touch each other externally, hence the smaller circle is incircle of the triangle formed by common tangents.

Q. The equation of incircle of the triangle formed by common tangents to the circles x2+y2=4 and x2+y2−6x+8=0 is

x2+y2=1

x2+y2−6x+8=0

x2+y2−6x+9=0