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area of quadrilateral

Source: 3rd National Women´s Contest of Mexican Mathematics Olympiad 2024 , level 1+2 p5

June 14, 2024
Mexicogeometry

Problem Statement

Consider the acute-angled triangle ABCABC. The segment BCBC measures 40 units. Let HH be the orthocenter of triangle ABCABC and OO its circumcenter. Let DD be the foot of the altitude from AA and EE the foot of the altitude from BB. Additionally, point DD divides the segment BCBC such that BDDC=35\frac{BD}{DC} = \frac{3}{5}. If the perpendicular bisector of segment ACAC passes through point DD, calculate the area of quadrilateral DHEODHEO.
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