regular pentagon The film strip shows the steps in the construction of the regular pentagon.

Copy this straight edge and compass construction for yourself and explain why it produces a regular pentagon.

The description of the construction below, and the information in the notes, should help you to explain the construction.
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Here are the steps shown in the film sequence:
1. Draw a circle C1 centre O diameter PQ.

The circle C1 has radius 1 unit what is its equation?

2. Draw the perpendicular bisector of PQ cutting PQ at O and C1 at A and Y.

3. Draw perpendicular bisectors of PO and OQ cutting PQ at R and S.

Find the length YS

4. Draw circles C2 and C3 centres R and S and radii RO and SO.

5. Join R and S to the point Y cutting C2 at T and U and C3 at V and W.

6. Draw circle C4 centre Y radius YW=YU cutting C1 at D and C.

What is the equation of C4? Find the value of y at the intersection of C1 and C4.

7. Draw circle C5 centre Y radius YT=YV cutting C1 at E and B.

What is the equation of C5? Find the value of y at the intersection of C1 and C5.

8. Join AB, BC, CD, DE, EA.

How would you adapt this construction to produce a regular decagon?