Circles

• THEOREM 1 The straight line drawn from the centre of a circle perpendicular to a chord bisects the chord.

          THEOREM 2 The line joining the centre of a circle and the mid-point of a chord is perpendicular to the chord.

　  Java                                      GSP

• THEOREM 3  Equal chords of a circle are equidistant from the centre.

           THEOREM 4 Chords which are equidistant from the centre of a circle are equal.

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• THEOREM 5 The angle at the centre standing on any arc of a circle is twice the angle at the circumference standing on the same arc.

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• THEOREM 6 The angle in a semi-circle is a right angle.

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• THEOREM 7 Angles in the same segment are equal.

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• THEOREM 8 The opposite angles of a cyclic quadrilateral are supplementary.

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• THEOREM 9 The one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior angle.

      Java                                          GSP