WOLFRAM|DEMONSTRATIONS PROJECT

1992 CMO Problem: Cocircular Orthocenters

P

1

P

2

P

3

P

4

Let

P

1

,

P

2

,

P

3

,

P

4

be distinct points on a circle (black) centered at

O

1234

. Let

H

123

be the orthocenter of triangle

P

1

P

2

P

3

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