#### You may also like ### Fitting In

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ ### Triangle Midpoints

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle? ### Three Way Split

Take any point P inside an equilateral triangle. Draw PA, PB and PC from P perpendicular to the sides of the triangle where A, B and C are points on the sides. Prove that PA + PB + PC is a constant.

# Tetrahedra Tester

##### Age 14 to 16Challenge Level

What are the limitations on the lengths of the sides of any triangle?

Look at different cases.

If the base is a 4 by 5 by 6 triangle, what size can the other faces be?

How many different tetrahedra can have as its base a 4 by 5 by 6 triangle?

Can you find 8 or more possible tetrahedra?

How will you know when you have them all?