![]() If the intersection of any two chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then ab = cd.Among all the circles with a chord AB in common, the circle with minimal radius is the one with diameter AB.The diameter is the longest chord of the circle.An inscribed angle subtended by a diameter is a right angle (see Thales' theorem).For a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.If two angles are inscribed on the same chord and on opposite sides of the chord, then they are supplementary.If two angles are inscribed on the same chord and on the same side of the chord, then they are equal.If a central angle and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle.The line segment through the centre bisecting a chord is perpendicular to the chord.A perpendicular line from the centre of a circle bisects the chord. ![]()
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