The proof follows by realizing that points (C,D,Q,E) form a harmonic division. Then, lines (PC,PD,PQ,PE), passing through these points, form a harmonic bundle of lines. But PQ and PR are, per construction, orthogonal at P. Hence these lines bisect the angle of the two others: ang(CPD).

Harmonic_Bundle.html

Todhunter, I.

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