Two equal circles that generate a perfect square
Each circle drawn on the other's centre; their axes cross at four right angles
A single pen proposition on intersecting circles. If two circles cut one another so that the circumference of each passes through the centre of the other, the circles are equal; the lines joining the two intersection points and joining the two centres cross at four right angles; and the circle drawn on the two centres is divided into four equal parts, yielding a perfect square. The construction is drawn as two overlapping circles with a cross at the lower left of the sheet.
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Equal intersecting circles yield a perfect square
Two circles cut one another so that the circumference of each falls on the centre of the other; therefore the circles are equal. The line through the two intersections and the line joining the two centres cross at four right angles, and the circle drawn on the two centres is split into four equal parts, forming a perfect square.