MathDB

Three points

A,B,C

are such that

B \in ]AC[

. On the side of

AC

we draw the three semicircles with diameters

[AB], [BC]

and

[AC]

. The common interior tangent at

B

to the first two semi-circles meets the third circle in

E

. Let

U

and

V

be the points of contact of the common exterior tangent to the first two semi-circles. Denote the area of the triangle

ABC

S(ABC)

. Evaluate the ratio

R=\frac{S(EUV)}{S(EAC)}

as a function of

r_1 = \frac{AB}{2}

and

r_2 = \frac{BC}{2}

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