MathDB

concurrency of reflected arcs of circumcircle

Source: 2015 NZOMC Camp Selections p3

January 10, 2021

geometrycircumcirclearcconcurrencyconcurrent

Problem Statement

Let

ABC

be an acute angled triangle. The arc between

A

and

B

of the circumcircle of

ABC

is reflected through the line

AB

, and the arc between

A

and

C

of the circumcircle of

ABC

is reflected over the line

AC

. Obviously these two reflected arcs intersect at the point

A

. Prove that they also intersect at another point inside the triangle

ABC