GRADE 11: EUCLIDEAN GEOMETRY

In this program, you will: 1. Accept results established in earlier grades as axioms that a tangent to a circle is perpendicular to the radius drawn to the point of contact 2. Then investigate and prove the theorems of the geometry of circles: • The line drawn from the centre of a circle perpendicular to a chord bisects the chord • The line drawn from the centre of a circle to the midpoint of a chord is perpendicular to the chord • The perpendicular bisector of a chord passes through the centre of the circle • The angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circle (on the same side of the chord as the centre) • Angles subtended by a chord of the circle, on the same side of the chord, are equal • The opposite angles of a cyclic quadrilateral are supplementary • Two tangents drawn to a circle from the same point outside the circle are equal in length • The angle between the tangent to a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment Use the above theorems and their converses, where they exist, to solve riders