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Circumcenter lies on circumcircle.

Source: Argentina Cono Sur TST 2024 P3

August 9, 2024

geometrycircumcircle

Problem Statement

Let

ABC

be an acute triangle. The point

B'

of the line

CA

is such that

A

,

C

,

B'

are in that order on the line and

B'C=AB

; the point

C'

of the line

AB

is such that

A

,

B

,

C'

are in that order on the line and

C'B=AC

. Show that the circumcenter of triangle

AB'C'

belongs to the circumcircle of triangle

ABC

.

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