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# Triangle Midpoints

Draw any triangle, find the midpoints, and join them.

What do you notice?

How can this help you solve the problem in reverse, starting with the midpoints and constructing the triangle?

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Age 14 to 16

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Draw any triangle, find the midpoints, and join them.

What do you notice?

How can this help you solve the problem in reverse, starting with the midpoints and constructing the triangle?

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

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second wall. At what height do the ladders cross?