MathDB

Let

\omega

and

\Omega

be circles of radius

1

and

R>1

respectively that are internally tangent at a point

P

. Two tangent lines to

\omega

are drawn such that they meet

\Omega

at only three points

A

B

, and

C

, none of which are equal to

P

. If triangle

ABC

has side lengths in a ratio of

3:4:5

, find the sum of all possible values of

R

.
Proposed by Connor Gordon

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