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Part of 2013 Bosnia Herzegovina Team Selection Test

Problems(1)

Right triangle parallel lines

Source: Bosnia and Herzegovina TST 2013 problem 1

5/20/2013
Triangle ABCABC is right angled at CC. Lines AMAM and BNBN are internal angle bisectors. AMAM and BNBN intersect altitude CHCH at points PP and QQ respectively. Prove that the line which passes through the midpoints of segments QNQN and PMPM is parallel to ABAB.
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