Constructions

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

Explain how to construct a regular pentagon accurately using a straight edge and compass.

Describe how to construct three circles which have areas in the ratio 1:2:3.

Draw a line (considered endless in both directions), put a point somewhere on each side of the line. Label these points A and B. Use a geometric construction to locate a point, P, on the line, which is equidistant from A and B.

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Can you reproduce the Yin Yang symbol using a pair of compasses?