It’s no wonder that farmers with fields in the plains surrounding Stonehenge, in southern England, face late-summer mornings with dread. On any given day at the height of the growing season, as many ...

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The second shape is not a cyclic quadrilateral. One corner does not touch the circumference. The opposite angles in a cyclic quadrilateral add up to 180°.

More simply, angles in the same segment are equal. Let the obtuse angle MOQ = \(2x\). Using the circle theorem, the angle at the centre is twice the angle at the circumference. Angle MNQ = \(x\) and ...

Summary We state and prove a surprising incidence theorem that was discovered with the help of a computer graphics program. The theorem involves sixteen points on ten lines and five circles; our proof ...