A triangle ABC is inscribed in a circle ω.
A variable line ℓ chosen parallel to BC meets segments AB, AC at points D, E respectively, and meets ω at points K, L (where D lies between K and E).
Circle γ1 is tangent to the segments KD and BD and also tangent to ω, while circle γ2 is tangent to the segments LE and CE and also tangent to ω.
Determine the locus, as ℓ varies, of the meeting point of the common inner tangents to γ1 and γ2.(Russia) Vasily Mokin and Fedor Ivlev geometrycircumcirclegeometric transformationtrigonometryconicsparabola