The orthocentre H, circumcentre O, the incentre I, and points B and C all lie on the top of the dunce’s spherical head. What is the angle α?
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Solution
The angle α is 60°.
![](https://mirangu.com/wp-content/uploads/2024/05/DunceCapSol.jpg)
Note the only two of the three special triangle points are needed to derive the result.