MathDB

5

Part of 2015 China Northern MO

Problems(1)

converse of orthocenter property, given 3 pairs of equal angles

Source: China Northern MO 2015 10.5 11.5 CNMO

10/28/2022
As shown in figure , points D,E,FD,E,F lies the sides ABAB, BCBC , CACA of the acute angle △ABC\vartriangle ABC respectively. If ∠EDC=∠CDF\angle EDC = \angle CDF, ∠FEA=∠AED\angle FEA=\angle AED, ∠DFB=∠BFE\angle DFB =\angle BFE, prove that the CDCD, AEAE, BFBF are the altitudes of △ABC\vartriangle ABC. https://cdn.artofproblemsolving.com/attachments/3/d/5ddf48e298ad1b75691c13935102b26abe73c1.png
geometryorthocenterequla angles