Matric Maths - Geometry Proof 1. Midpoint Chord Theorem (⊥ line drawn from centre bisects chord)

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In this video we look at the 1st of 6 examinable proofs for the Matric Mathematics exam. This Midpoint Chord Theorem which says that the line drawn from the centre of a circle perpendicular to a chord bisects the chord. Here I make the necessary constructions, say what we need to prove and then proceed to prove it using the diagram.

According to the Department of Education, the following proofs of theorems are examinable:
• Midpoint Chord Theorem: The line drawn from the centre of a circle perpendicular to a chord bisects the chord
• Angle at Centre Theorem: 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);
• Cyclic Quad Theorem: The opposite angles of a cyclic quadrilateral are supplementary;
• Tan-chord Theorem: 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;
• Prop theorem: A line drawn parallel to one side of a triangle divides the other two sides proportionally;
• Similar Triangle Theorem: Equiangular triangles are similar.

Here is the link to the Matric Examination Guidelines which contain the proofs and reasons you need to know for Geometry.

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About the teacher

Nick Hiltermann has a Bachelor of Science from the University of Cape Town where he majored in Genetics, Microbiology and Biochemistry. He also has a Bachelor of Commerce majoring in Information Systems and Marketing. He completed electives in Accounting, Economics, Maths (financial and scientific), Physics and Chemistry. He is has tutored students from Level 1 up to A Levels assisting them in the Cambridge Syllabus.

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