### Two Trees

Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?

### Golden Triangle

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

### Strange Rectangle

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

# Chord

##### Stage: 5 Challenge Level:

Three circles all of radius 2 cm touch as shown in the diagram.

A straight line $AG$ is tangential to the third circle, meeting the middle circle at $H$ and $I$.

How long is $HI$?

What if there are four or more circles?