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A problem in the math test paper of Shantou senior high school entrance examination in 2009 ... Who can help me solve it?
(1) Prove that the point where OH is vertical and AB intersects AB and H connects AO, BO and OC;

It can be proved that six small triangles are congruent.

(2) Since the distance from point O to three sides is equal (S Yin =Sofc+Soch), it is assumed that OD passes through BC and F, and OE passes through AC and G, as long as it is proved that FC+CG is equal to the side length of a triangle.

It can be proved that the passing angles of triangle ODC and triangle AOG are identical, that is, DC=AG, that is, FC+CG=AC.