Line joining tangent circles

A circle of radius 4 is tangent to a circle of radius 9, and a line is tangent to both circles at A and B. Find |AB|.

Equiangular hexagon

Let ABCDEF be an equiangular hexagon. If |AB|=3, |BC|=5, and |DE|=7, find |EF|.

Spider on a ladder

A 4 meter ladder leans against a wall, the base 1 meter from the wall. A spider is sitting at the midpoint of the ladder. If the ladder slides down the wall, how far will the spider travel?

Viewing angle of a painting

The top of a painting is 4 feet above eye level, and the bottom is 1 foot above eye level. How far should one stand from the wall to get the widest view?

Equilateral triangle in a circle

Let ABC be an equilateral triangle inscribed in a circle, and P a point on the arc AB. Find |CP| given that |AP|=3 and |BP|=4.