5

Part of 2024 Mexican Girls' Contest

Problems(1)

area of quadrilateral

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

Consider the acute-angled triangle

ABC

BC

measures 40 units. Let

H

be the orthocenter of triangle

ABC

O

its circumcenter. Let

D

be the foot of the altitude from

A

E

the foot of the altitude from

B

. Additionally, point

D

divides the segment

BC

\frac{BD}{DC} = \frac{3}{5}

. If the perpendicular bisector of segment

AC

passes through point

D

, calculate the area of quadrilateral

DHEO