Fish in a Bowl
Geometry
Level
3
An acute triangle has a circumcircle, as shown. Minor arcs are reflected about each side of the triangle.
Do the three reflected arcs intersect at the same point?
Never
Yes, at a point which is not a triangle's center
Yes, at the triangle's centroid
Yes, at the triangle's orthocenter
Yes, at the triangle's circumcenter
Sometimes
Yes, at some other triangle's center
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The reflection of the orthocentre about any side of a triangle lies on the circumcircle of the triangle