Wolfram Demonstrations Project

Let

be distinct points on a circle (black) centered at

. Let

be the orthocenter of triangle

and so on. You can show that the four orthocenters are cocircular and the circle (green) has the same radius as the original circle.

This Demonstration is based on a problem from the 2nd Section of the Chinese Math Olympic National Final in 1992.

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1992 CMO Problem: Cocircular Orthocenters