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Two Triangles

Age 11 to 14 Short
Challenge Level

In the diagram, triangle ABC is isosceles with AB = BC.

The line AP is drawn so that it meets the side BC at a right angle.

Prove that the angle marked $a$ is half the size of the angle marked $b$.

This problem is taken from 1000 Problems to Enjoy

You can find more short problems, arranged by curriculum topic, in our short problems collection.