Let Circle A be external tangent to Circle B. Let Circle C be external tangent to both Circle A and B. All three circles are external tangent to a line. Prove that for any given radius of Circle A and B, for example, x and y, respectively, the radius of the Circle C with radius z can be expressed as [1/sqrt(x)]+[1/sqrt(y)]= [1/sqrt(z)]

(Google Images)
## Comments

Sort by:

TopNewestUse descartes' circle theorem. – Deeparaj Bhat · 1 year ago

Log in to reply

– Raymond Park · 1 year ago

Any other way?Log in to reply

We first prove the following lemma:

Using this lemma, we get the following proof:

– Deeparaj Bhat · 1 year agoLog in to reply

@Raymond Park Was this helpful? – Deeparaj Bhat · 1 year ago

Log in to reply

– Raymond Park · 1 year ago

Well done!Log in to reply