### The Eyeball Theorem

Two tangents are drawn to the other circle from the centres of a pair of circles. What can you say about the chords cut off by these tangents. Be patient - this problem may be slow to load.

### Hexy-metry

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

# Area I'n It

##### Stage: 5 Challenge Level:

Triangle $ABC$ has altitudes $h_1$, $h_2$ and $h_3$.

The radius of the inscribed circle is $r$, while the radii of the escribed circles are $r_1$, $r_2$ and $r_3$ respectively.

Prove:

$$$\frac{1}{r} = \frac{1}{h_1} + \frac{1}{h_2} + \frac{1}{h_3} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}.$$$