Two circles with equal radii are intersecting at the points (0, 1) and (0, -1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :

Question

Two circles with equal radii are intersecting at the points (0, 1) and (0, -1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is : (A) 1 (B) √2 (C)  2 √2 (D) 2

Tardigrade Admin · Accepted Answer

In Δ APO ((√2r/2))2 + 12 =r2 ⇒ r= √2 So distance between centres = √2 r = 2

Q. Two circles with equal radii are intersecting at the points $(0, 1)$ and $(0, - 1)$ . The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :

$1$

$2$

$22$

$2$

In $Δ A PO$
$(\frac{2 r}{2})^{2} + 1^{2} = r^{2}$
$\Rightarrow r = 2$
So distance between centres $= 2 r = 2$

Q. Two circles with equal radii are intersecting at the points (0,1) and (0,−1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :

1

2​

22​

2

In ΔAPO (22​r​)2+12=r2 ⇒r=2​ So distance between centres =2​r=2

Q. Two circles with equal radii are intersecting at the points $(0, 1)$ and $(0, - 1)$ . The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :

$1$

$2$

$22$

$2$

In $Δ A PO$
$(\frac{2 r}{2})^{2} + 1^{2} = r^{2}$
$\Rightarrow r = 2$
So distance between centres $= 2 r = 2$