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3 points coincide, symmetric of antidiametric wrt midpoint is fixed

Source: TOT 410 1994 Spring O S1 - Tournament of Towns

June 12, 2024

geometrysymmetry

Problem Statement

A triangle

ABC

is inscribed in a circle. Let

A_1

be the point diametrically opposed to

A

A_0

be the midpoint of the side

BC

and

A_2

be the point symmetric to

A_1

with respect to

A_0

; the points

B_2

and

C_2

are defined in a similar way starting from

B

and

C

. Prove that the three points

A_2

B_2

and

C_2

coincide.
(A Jagubjanz)