You may also like

problem icon

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

problem icon

Triangle Midpoints

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

problem icon

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.

Circumnavigation

Age 14 to 16 Challenge Level:

Triangle inscribed in a circle

The sides of a triangle are 25, 39 and 40 units of length.

Find the diameter of the circumscribed circle.