A triangle ABC is given together with an arbitrary circle ω. Let α be the reflection of ω with respect to A, β the reflection of ω with respect to B, and γ the reflection of ω with respect to C. It is known that the circles α,β,γ don't intersect each other.
Let P be the meeting point of the two internal common tangents to β,γ (see picture). Similarly, Q is the meeting point of the internal common tangents of α,γ, and R is the meeting point of the internal common tangents of α,β.
Prove that the triangles PQR,ABC are congruent. geometrycongruent trianglesgeometric transformationreflection