MathDB

Prove that BO perpendicular to AC if DE parallel to AC

Source: Mumbai Region RMO 2014 Problem 3

December 7, 2014

trigonometrygeometryangle bisector

Problem Statement

Let

ABC

be an acute-angled triangle in which

\angle ABC

is the largest angle. Let

O

be its circumcentre. The perpendicular bisectors of

BC

and

AB

meet

AC

X

and

Y

respectively. The internal angle bisectors of

\angle AXB

and

\angle BYC

meet

AB

and

BC

D

and

E

respectively. Prove that

BO

is perpendicular to

AC

DE

is parallel to

AC