MathDB

OI is perpendicular to DE

Source: China TST 1988, problem 3

June 27, 2005

geometrycircumcircleincentergeometry solved

Problem Statement

In triangle

ABC

\angle C = 30^{\circ}

O

and

I

are the circumcenter and incenter respectively, Points

D \in AC

and

E \in BC

, such that

AD = BE = AB

. Prove that

OI = DE

and

OI \bot DE