MathDB

Area ratio is equal to length ratio

Source: Baltic Way 1999

December 23, 2010

geometryratiogeometry proposed

Problem Statement

Let

ABC

be an isosceles triangle with

AB=AC

. Points

F

and

C

lie on the sides

AB

and

DE

, respectively. The line passing through

G

and parallel to

\frac{[DBCG]}{[FBCE]}=\frac{AD}{DE}

meets the line

DE

at

F

. The line passing through

C

and parallel to

AB

meets the line

DE

at

G

. Prove that

\frac{[DBCG]}{[FBCE]}=\frac{AD}{DE}

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