OR Theorem 1 The line drawn from the centre of a circle, perpendicular to a chord, bisects the chord. The above theorems and their converses, where they exist, are used to prove riders. The angle between the tangent of a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment. Two tangents drawn to a circle from the same point outside the circle are equal in length (If two tangents to a circle are drawn from a point outside the circle, the distances between this point and the points of contact are equal).
The opposite angles of a cyclic quadrilateral are supplementary. Angles subtended by an arc or chord of the circle on the same side of the chord are equal. The angle subtended by an arc at the centre of a circle is double the angle subtended by the same arc at the circle (on the same side of the arc as the centre). The perpendicular bisector of a chord passes through the centre of the circle. The line drawn from the centre of a circle perpendicular to the chord bisects the chord. In this guide, only FOUR examinable theorems are proved. However, there are four theorems whose proofs are examinable (according to the Examination Guidelines 2014) in grade 12. 4 SUMMARY OF THEOREMS 4.2 Definitions 4.2 Angles in circles 4.2 Cyclic Quadrilaterals 4 PROOF OF THEOREMS All SEVEN theorems listed in the CAPS document must be proved. A chord divides a circle into two segments Tangent A tangent is a line that makes contact with a circle at one point on the circumference (AB is a tangent to the circle at point P). Segment A segment is the part of the circle that is cut off by a chord.
A Diameter is the length of a straight line segment from one point on the circumference to another point on the circumference, that passes through the centre of the circle. Radius A radius is any straight line from the centre of the circle to a point on the circumference Diameter A diameter is a special chord that passes through the centre of the circle. CIRCLES 4 TERMINOLOGY Arc An arc is a part of the circumference of a circle Chord A chord is a straight line joining the ends of an arc.
#CIRCLE GEOMETRY GRADE 11 PDF FULL#
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