Using straight edge and compass, divide given circle into 9 parts of equal area?

Answer 1

Draw a perpendicular pair of diameters in the circle, and divide them into thirds. Then draw in 5 circles of diameters 1/3 of the original diameter. Each of the circles have 1/9th the area of the original, leaving 4 equal odd shaped pieces. A moment's thought shows that they're also of the same area as the small circles.

Answer 2

Draw a line from the center of the circle to any point on the circle.

Adjust your compass to an angle of 40 degrees. (360/9=40)

Place the point of the compass on the point where the initial line intersects the circle, and inscribe an arc that intersects the circle. The point where it intersects is the first of the remaining points that divides the circle.

Place the point of the compass on the new intersection and repeat until you have inscribed arcs through the circle equaling 9 parts.

Draw lines from the center of the circle to the points on the circle where the arcs intersect.

Answer 3

360 degrees / 9 = 40 degrees

First, draw a line from the center of the circle out to the edge.

Next, draw a line 40 off of it in either direction also from the center to the edge.

Repeat until there are 9 lines.