Let the excircle of the triangle
lying opposite to
touch its side
at the point
. Define the points
and
analogously. Suppose that the circumcentre of the triangle
lies on the circumcircle of the triangle
. Prove that the triangle
is right-angled.
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Let the excircle of the triangle $ABC$ lying opposite to $A$ touch its side $BC$ at the point $A_1$. Define the points $B_1$ and $C_1$ analogously. Suppose that the circumcentre of the triangle $A_1B_1C_1$ lies on the circumcircle of the triangle $ABC$. Prove that the triangle $ABC$ is right-angled.
Školjka