Forum Geometricorum, 1 (2001) 81 -- 90.

Abstract: The pedal triangle of a point P with respect to a given triangle ABC casts equal shadows on the side lines of ABC if and only if P is the internal center of similitude of the circumcircle and the incircle of triangle ABC, or the external center of similitude of the circumcircle with one of the excircles. We determine the common length of the equal shadows. More generally, we construct the point the shadows of whose pedal triangle are proportional to given p, q, r. Many interesting special cases are considered.

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