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Bangladesh Mathematical Olympiad 2020 Final

Source: BdMO 2020 Final Primary Category Problem 2

August 30, 2020

Pure geometrygeometry

Problem Statement

Consider rectangle

ABCD

E

is the mid-point of

AD

and

F

is the mid-point of

ED

CE

cuts

AB

G

and

BF

cuts

CD

H

point. We can write ratio of areas of

BCG

and

BCH

triangles as

\frac{m}{n}

. Find the value of

10m + 10n + mn