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distance of circumcenters = AC

Source: 2021 Sharygin Finals grade VIII p4

August 1, 2021

geometryCircumcenterdistance

Problem Statement

Let

A_1

and

C_1

be the feet of altitudes

AH

and

CH

of an acute-angled triangle

ABC

. Points

A_2

and

C_2

are the reflections of

A_1

and

C_1

about

AC

. Prove that the distance between the circumcenters of triangles

C_2HA_1

and

C_1HA_2

equals

AC