is any point on the side
of the triangle
.
are the radii of the circles inscribed in
.
is the radius of the circle on the opposite side of
to
, touching the three sides of
and the extensions of
and
. Similarly,
and
. Prove that
.
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$M$ is any point on the side $AB$ of the triangle $ABC$. $r,r_1,r_2$ are the radii of the circles inscribed in $ABC,AMC,BMC$. $q$ is the radius of the circle on the opposite side of $AB$ to $C$, touching the three sides of $AB$ and the extensions of $CA$ and $CB$. Similarly, $q_1$ and $q_2$. Prove that $r_1r_2q=rq_1q_2$.
Školjka