Question

5. The distance between the centres of the two circles
of radii r, and r, is d. They will touch each other
internally if:
(a) d = r, or r,
(b) d = r, +r2
(c) d = r,-1(r,>r) (d) d = VI,​

Answer 1

d =  r₁ - r₂    if r₁ > r₂  or & r₂- r₁    if r₂ > r₁ if Circle stouch each other internally

Step-by-step explanation:

Let say circle of radius

r₁  & r₂  touches at point P

if we Draw a Tangent at that point P

then it will be perpendicular to line from point P touching the center of circle

=> center of both circles would be Colineae

Distance of one Circle Center  = r₁

Distance of other  Circle Center = r₂

distance between the centers of the two circles d =  r₁ - r₂    if r₁ > r₂

& r₂- r₁    if r₂ > r₁

if Circle touches externally then

d  = r₁ + r₂

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Answer 2

$d = r_1 + r_2$

Step-by-step explanation:

Let the two circles have centers at A and B.

The distance between the centers of two circles of radii $r_1$ and $r_2$ is d.

Now, if the two circles touch each other at point P, then AP = $r_1$ and BP = $r_2$.

Therefore, the distance between the two centers A and B i.e.

AB = d = AP + BP = $r_1 + r_2$

⇒ $d = r_1 + r_2$ (Answer)