Question 39826
PROBLEM IS NOT SPECIFIC.....SEE BELOW
3 circles on the same straight line...
MEANS WHAT?...CENTRES ON SAME LINE?ASSUMING SO...
, the 1st with a radius of R1=16 cm,
OK
 the 2nd with a radius of R2=9cm,
WHARE?INSIDE THE OTHER CIRCLE?HOW FAR ?OR TOUCHING?OR OUT SIDE?HOW FAR?
 is there a way to find the radius of the 3rd circle which sits in between the other two?
IF THE ABOVE 2 ARE CLARIFIED WE CAN ..
IF 2 CIRCLES ARE  SUCH THAT THEIR CENTRE ARE AT A DISTANCE (D)WHICH IS  MORE THAN 16+9=25 CM AWAY...SAY...30 CM..THEN WE CAN DRAW A CIRCLE OF 5 CM DIA OR 2.5 CM RADIUS TOUCHING BOTH
.IN GENERAL IF D >R1+R2...WE CAN DRAW A CIRCLE OF RADIUS ={D-(R1+R2)}/2

ON THE OTHER HAND IF THE 2 CIRCLES ARE SUCH THAT THEIR CENTRES ARE AT DISTANCE (D)WHICH IS  LESS THAN 16-9=7 CM AWAY...SAY...5 CM..THEN WE CAN DRAW A CIRCLE OF   2 CM DIA OR 1 CM RADIUS TOUCHING BOTH
.IN GENERAL IF D <R1-R2...WE CAN DRAW A CIRCLE OF RADIUS ={D-(R1-R2)}/2