For-two-co-planer-circles-to-be-tangent-necessary-and-sufficient-condition-is-I-think-the-distance-between-the-centers-of-circles-must-be-equal-to-r-1-r-2-or-r-1-r-2-where-r

Question Number 4077 by Rasheed Soomro last updated on 28/Dec/15

For two co - planer circles to be tangent

necessary and sufficient condition is,

I think

the distance between the centers of

circles must be equal to r_{1} + r_{2} or ∣ r_{1} - r_{2} ∣,

where r_{1} and r_{2} are the radii of the circles .

If circles belong to different planes, what

is necessary and sufficient condition for

being tangent ?

Commented by Yozzii last updated on 27/Dec/15

Commented by Yozzii last updated on 27/Dec/15

C i r c l e s c a n t o u c h i n t e r n a l l y a s a b o v e .

T h e b r o k e n l i n e s a r e r a d i i .

\Rightarrow r_{1} + r_{2} \neq C_{1} C_{2}

Commented by RasheedSindhi last updated on 28/Dec/15

You are right! I think I should add

a word “ {externally}^{″} in my question

then .

Commented by Rasheed Soomro last updated on 28/Dec/15

If we {don}^{'} t specify^{'} {externally}^{'} then

the necessary and sufficient condition

for being tangent of two circles should

be, I think

r_{1} + r_{2} = C_{1} C_{2} ∣ ∣ r_{1} - r_{2} ∣= C_{1} C_{2}

I have corrected the statement of the

question .