MathDB

computational with circumcenter, AB =1, AO = AC = 2, OD = OE, BD =\sqrt2 EC

Source: December 2020 Ukraine Geometry Olympiad VIII p5 , IX p4

December 21, 2020

geometryCircumcenterequal segments

Problem Statement

Let

O

is the center of the circumcircle of the triangle

ABC

. We know that

AB =1

and

AO = AC = 2

. Points

D

and

E

lie on extensions of sides

AB

and

AC

beyond points

B

and

C

respectively such that

OD = OE

and

BD =\sqrt2 EC

. Find

OD^2