Let
be a triangle,
its incircle and
three circles orthogonal to
passing through
and
respectively. The circles
and
meet again in
; in the same way we obtain the points
and
. Prove that the radius of the circumcircle of
is half the radius of
.
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Let $ABC$ be a triangle, $\Omega$ its incircle and $\Omega_{a}, \Omega_{b}, \Omega_{c}$ three circles orthogonal to $\Omega$ passing through $(B,C),(A,C)$ and $(A,B)$ respectively. The circles $\Omega_{a}$ and $\Omega_{b}$ meet again in $C'$; in the same way we obtain the points $B'$ and $A'$. Prove that the radius of the circumcircle of $A'B'C'$ is half the radius of $\Omega$.
Školjka