Let be ABC an acute-angled triangle. Consider point P lying on the opposite ray to the ray BC such that ∣AB∣=∣BP∣. Similarly, consider point Q on the opposite ray to the ray CB such that ∣AC∣=∣CQ∣. Denote J the excenter of ABC with respect to A and D,E tangent points of this excircle with the lines AB and AC, respectively. Suppose that the opposite rays to DP and EQ intersect in F=J. Prove that AF⊥FJ. geometryexcircleTriangleperpendicular linesnational olympiad