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?


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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

$If we {don}^{'} t specify^{'} {externally}^{'} then$ $the necessary and sufficient condition$ $for being tangent of two circles should$ $be, I think$ $r_{1} + r_{2} = C_{1} C_{2} ∣ ∣ r_{1} - r_{2} ∣= C_{1} C_{2}$ $I have corrected the statement of the$ $question .$
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