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?

Solution

The angle α is 60°.

Note the only two of the three special triangle points are needed to derive the result.

The orthocentre H, cicumcentre 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? https://t.co/bowssrWIpJ By @MarshallWBuck pic.twitter.com/VsvuY8x3TW

— Mirangu (@Mirangu1) May 9, 2024