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S_{AOK} = S_{AOB} + S_{DOK}, areas, starting with a trapezoid

Source: Oral Moscow Geometry Olympiad 2015 grades 10-11 p3

August 6, 2019

areastrapezoidgeometry

Problem Statement

O

is the intersection point of the diagonals of the trapezoid

ABCD

. A line passing through

C

and a point symmetric to

B

with respect to

O

, intersects the base

AD

at the point

K

. Prove that

S_{AOK} = S_{AOB} + S_{DOK}