MathDB

2022 Geo Div 1 P4 (Div 2 P8)

Source:

February 28, 2022

geometry

Problem Statement

Let

A

and

B

be points on circle

\Gamma

such that

AB=\sqrt{10}.

Point

C

is outside

\Gamma

such that

\triangle ABC

is equilateral. Let

D

be a point on

\Gamma

and suppose the line through

C

and

D

intersects

AB

and

\Gamma

again at points

E

and

F \neq D.

It is given that points

C, D, E, F

are collinear in that order and that

CD=DE=EF.

What is the area of

\Gamma?

Proposed by Kyle Lee

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