MathDB

line passes through the intersection of two circumcircles, when <A=60^O

Source: StT. Petersburg 2019 9.6

May 1, 2019

geometryparallelogramangle bisectorcircumcircle

Problem Statement

The bisectors

BB_1

and

CC_1

of the acute triangle

ABC

intersect in point

I

. On the extensions of the segments

BB_1

and

CC_1

, the points

B'

and

C'

are marked, respectively So, the quadrilateral

AB'IC'

is a parallelogram. Prove that if

\angle BAC = 60^o

, then the straight line

B'C'

passes through the intersection point of the circumscribed circles of the triangles

BC_1B'

and

CB_1C'