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

Look Before You Leap

Can you spot a cunning way to work out the missing length?

Triangle Midpoints

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

It Depends on Your Point of View!

Age 14 to 16
Challenge Level
similar triangles
Imagine your eye is at the top of the blue line at a height of $h$. You want the image to appear to be standing straight up where the red line is, a distance $d$ horizontally from your eye.
For the yellow point to appear a height $x$ above the ground, it needs to be drawn a distance $y$ along the ground from the base of the red line.

If you knew $h$, $d$ and $x$, how could you work out $y$?