### Right Time

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

### Isosceles

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

# 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.