Draw a circle A with perpendicular lines going through it (EC, DA).

Construct the midpoint of AB and label it C.

Draw a line from C to D.

Using CD as radius and C as center, draw an arc to line BA (arc DE).

Draw line segment DE.

Using DE as radius and D as center, draw an arc intersecting circle A at F and G.

Draw DF and DG.

Using FD or GD as radius and F and G as centers, draw arcs intersecting the circle at D, H and I.

Draw FH and GI.

Draw HI.

HIGDF is a regular pentagon.

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