Let Aa, Ba, Ca the contact points between the A-excircle and the sides. Define analogously Ab, Bb, Cb, Ac, Bc, Cc. Let X = CbAbÇAcBc, and define analogously Y, Z. The triangle XYZ, the medial triangle of ABC and the excentral triangle are perspective with common center the Mittenpunkt Mt, and XYZ and the excentral triangle are homothetic.