An acute triangle is inscribed in a circle. The resulting three minor arcs of the circle are reflected about the corresponding sides of the triangle.

Question

An acute triangle is inscribed in a circle. The resulting three minor arcs of the circle are reflected about the corresponding sides of the triangle. Are the reflected arcs concurrent?

Source: Problem Solving Through Problems by Loren C. Larson

Answer 1

It is a known property that, given a triangle $T$, the symmetric of the orthocenter with respect to a side of $T$ belongs to the circumcircle.

This can be viewed as a consequence of the following properties ($H$ denotes the orthocenter of $T$) :

1) The feet of the altitudes belong to the Euler circle of $T$

2) The homothety with center $H$ and ratio $2$ transforms the Euler circle into the circumcircle.

Hence the three arcs you mentioned must go through the orthocenter.

Answer 2

It is clear when reflections of the entire circum-circle are mirrored on each side they should concur at triangle orthocenter.. due to perpendicularity with each side.

EDIT1:

Among all perpendiculars to $AC$ choose one through B, repeat for 3 sides. Unique concurrency point must be the orthocenter. Other points of concurrency and new orthocenters would result by choice of other points for$ B$ as $ B_1,B_2$ &c on the same circumcircle.