MathDB

1991.10.2

Part of Kyiv City MO 1984-93 - geometry

Problems(1)

citerion / converse of a property of altitudes 1991 Kyiv City MO 10.2

Source:

7/19/2021
In an acute-angled triangle ABCABC on the sides ABAB, BCBC, ACAC, the points C1C_1, A1A_1, and B1B_1 are marked such that the segments AA1AA_1, BB1BB_1, CC1CC_1 intersect at some point OO and the angles AA1CAA_1C, BB1ABB_1A, CC1BCC_1B are equal. Prove that AA1AA_1, BB1BB_1, and CC1CC_1 are the altitudes of the triangle.
geometryaltitudesorthocenter