MathDB

Circle area ratio

Source: 2016 SDMO Middle School Problem 2

August 25, 2016

geometryratio

Problem Statement

Let

AB

be a diameter of a circle and let

C

be a point on

AB

with

2\cdot AC=BC

. Let

D

and

E

be points on the circle such that

DC\perp AB

and

DE

is a second diameter. What is the ratio of the area of

\triangle{DCE}

to the area of

\triangle{ABD}