If one of the diameters of the circle x2 + y2 - 2x - 6y + 6 = 0 is a chord to the circle with centre (2,1), then the radius of the circle is

Question

If one of the diameters of the circle x2 + y2 - 2x - 6y + 6 = 0 is a chord to the circle with centre (2,1), then the radius of the circle is (A) √3 (B) √2 (C) 3 (D) 2

Tardigrade Admin · Accepted Answer

Here, radius of sm aller circle, AC = √1 + 9- 6 = 2 Clearly, from the figure the radius of bigger circle r2 = 22 + [(2 - 1)2 + (1 - 3)2] r2=9 ⇒ r = 3

Q. If one of the diameters of the circle $x^{2} + y^{2} - 2 x - 6 y + 6 = 0$ is a chord to the circle with centre $(2, 1)$ , then the radius of the circle is

$3$

$2$

3

2

Here, radius of sm aller circle, AC = $1 + 9 - 6 = 2$
Clearly, from the figure the radius of bigger circle
$r^{2} = 2^{2} + [(2 - 1)^{2} + (1 - 3)^{2}]$
$r^{2} = 9 \Rightarrow r = 3$

Q. If one of the diameters of the circle x2+y2−2x−6y+6=0 is a chord to the circle with centre (2,1), then the radius of the circle is

3​

2​

3

2

Here, radius of sm aller circle, AC = 1+9−6​=2 Clearly, from the figure the radius of bigger circle r2=22+[(2−1)2+(1−3)2] r2=9⇒r=3

Q. If one of the diameters of the circle $x^{2} + y^{2} - 2 x - 6 y + 6 = 0$ is a chord to the circle with centre $(2, 1)$ , then the radius of the circle is

$3$

$2$

Here, radius of sm aller circle, AC = $1 + 9 - 6 = 2$
Clearly, from the figure the radius of bigger circle
$r^{2} = 2^{2} + [(2 - 1)^{2} + (1 - 3)^{2}]$
$r^{2} = 9 \Rightarrow r = 3$