Cyclic Quadrilaterals

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Grade 11 · Term 3

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About O/L Mathematics: O/L Mathematics covers number systems, algebra, geometry, trigonometry, and statistics across Grade 10 and 11.

• Opposite angles sum to 180 degrees: In a cyclic quadrilateral, angle A + angle C = 180 degrees and angle B + angle D = 180 degrees
• Converse: If opposite angles sum to 180 degrees, the quadrilateral is cyclic: If angle A + angle C = 180 degrees, then points A, B, C, D are concyclic
• Exterior angle equals interior opposite angle: In a cyclic quadrilateral, an exterior angle formed by extending one side equals the interior angle opposite to the adjacent interior angle. For example, if side AB is extended to E, then angle CBE = angle ADC
• Angles subtended by the same chord are equal: In a cyclic quadrilateral, angles that subtend the same chord from the circumference are equal. For example, angle ABD = angle ACD (both subtend AD)
• Sum of all interior angles: The sum of all four interior angles of any quadrilateral is 360 degrees. This is always true, but in a cyclic quadrilateral, it is consistent with the opposite angle sum property

Source: Idasara knowledge pack — english/OL_11/mathematics v16, short_notes: Lesson 21 - Cyclic Quadrilaterals

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