is a point on the semicircle diameter
, between
and
.
is the foot of the perpendicular from
to
. The circle
is the incircle of
, the circle
touches
and the semicircle, the circle
touches
and the semicircle. Prove that
and
have another common tangent apart from
.
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$C$ is a point on the semicircle diameter $AB$, between $A$ and $B$. $D$ is the foot of the perpendicular from $C$ to $AB$. The circle $K_1$ is the incircle of $ABC$, the circle $K_2$ touches $CD,DA$ and the semicircle, the circle $K_3$ touches $CD,DB$ and the semicircle. Prove that $K_1,K_2$ and $K_3$ have another common tangent apart from $AB$.
Školjka