Triangle centers constructed from O, H, and I
- Dear friends,
I have just put the following problem in the Inventory of POLYA:
Inventory015: Triangle centers constructed from O, H, and I (proposed
by Paul Yiu, 11/30/01).
This is Problem E2407 of the American Mathematical Monthly, proposed
Given the circumcenter O, the orthocenter H, and the incenter I of an
unknown triangle (T),
(a) locate by euclidean construction the Gergonne point and the
Lemoine point of T,
(b) locate the orthocenters of the pedal triangles of H and I.
Editorial Note: This problem is interesting because triangle (T)
cannot in general be constructed from the given points, but many
points related to (T), including those mentioned in this problem, can
be so constructed. The two solutions received are quite involved, so
we do not take the space here to print either of them.
Bibliography.  A.W.Walker, Problem E2407, American Mathematical
Monthly, 80 (1973) 316; editorial note, 81 (1974) 406.