@MISC{T_herethe, author = {Ha T}, title = {Here the rst term,,!}, year = {} }

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Abstract

No problem is ever permanently closed. The editor is always pleased to consider for publication new solutions or new insightsonpastproblems. 1492. [1989: 297; 1991: 50] Proposed by G.Tsintsifas, Thessaloniki, Greece. Let A 0 B 0 C 0 be a triangle inscribed in a triangle ABC, so that A 0 2 BC, B 0 2 CA, C 0 2 AB. Suppose also that BA 0 = CB 0 = AC 0. 1. If either the centroids G, G 0 or the circumcentres O, O 0 of the triangles coincide, prove that 4ABC is equilateral. 2.? If either the incentres I, I 0 or the orthocentres H, H 0 of the triangles coincide, characterize 4ABC. III. Solution to part2? byC.R.Pranesachar and B.J. Venkatachala,