2000 IMO Problems/Problem 6

Problem

Let $\overline{AH_1}$ , $\overline{BH_2}$ , and $\overline{CH_3}$ be the altitudes of an acute triangle $ABC$ . The incircle $\omega$ of triangle $ABC$ touches the sides $BC$ , $CA$ , and $AB$ at $T_1$ , $T_2$ , and $T_3$ , respectively. Consider the reflections of the lines $H_1H_2$ , $H_2H_3$ , and $H_3H_1$ with respect to the lines $T_1T_2$ , $T_2T_3$ , and $T_3T_1$ . Prove that these images form a triangle whose vertices line on $\omega$ .

Solution

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2000 IMO (Problems) • Resources
Preceded by Problem 5	1 • 2 • 3 • 4 • 5 • 6	Followed by Last Question
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2000 IMO Problems/Problem 6

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