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3 triangles with equal area, equilateral maybe

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1994 p5

February 20, 2020
geometryEquilateraltriangle areaequal areasaltitudes

Problem Statement

In an acute-angled triangle ABCABC, the altitudes AA1,BB1,CC1AA_1,BB_1,CC_1 intersect at point VV. If the triangles AC1V,BA1V,CB1VAC_1V, BA_1V, CB_1V have the same area, does it follow that the triangle ABCABC is equilateral?
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