Question-214683

Question Number 214683 by MATHEMATICSAM last updated on 16/Dec/24

Commented by MATHEMATICSAM last updated on 16/Dec/24

Circles C 1 and C 2 have equal radii and

are tangent to the same line XY . Circle

C 3 is tangent to C 1 and C 2 . Find

distance h, from the centre of C 3 to line

XY in terms of x and radii of the circles .

x is the distance between the centres of

C 1 and C 2 .

Answered by mr W last updated on 16/Dec/24

a = r a d i u s o f C 1 a n d C 2

b = r a d i u s o f C 3

{(h - a)}^{2} + {(\frac{x}{2})}^{2} = {(a + b)}^{2}

\Rightarrow h = a + \sqrt{{(a + b)}^{2} - \frac{x^{2}}{4}}

Commented by MATHEMATICSAM last updated on 16/Dec/24

Thanks sir :)