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concurrency wanted, feet of altitudes, intersection with circumcircle related

Source: Sharygin 2019 final 10 P5

August 15, 2019
geometrycircumcircleconcurrencyaltitudes

Problem Statement

Let AA1,BB1,CC1AA_1, BB_1, CC_1 be the altitudes of triangle ABCABC, and A0,C0A0, C0 be the common points of the circumcircle of triangle A1BC1A_1BC_1 with the lines A1B1A_1B_1 and C1B1C_1B_1 respectively. Prove that AA0AA_0 and CC0CC_0 meet on the median of ABC or are parallel to it
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