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# The locus of the centre of a circle which touches two given circles of different radii externally is

Asked by ankitraj875725 29th November 2018, 3:54 PM Let A and B are the given two circles with radii R1 and R2 respectively and their centres are F and G respectively.
Let C and D are variable circles so that each circle meet the given circles A and B externally.
Let r1 be the radius of circle C and P be its centre. Let r2 be the radius of circle D and Q be its centre.

PF = R1+r,  PG = R2+r1 ,   PF-PG = R1 - R2

QF = R1+r,  QG = R2+r2 ,  QF-QG = R1 - R2

Hence locus of centres of touching circles is  set of points so that the difference between the distances from two given
fixed points ( here F and G ) to the point in locus is  constant.

This locus is hyperbola and the fixed points F and G (Centers of given circles ) are foci of hyperbola
Answered by Expert 30th November 2018, 10:01 AM
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