Proof That a Line From a Point to the Centre of a Circle Bisects the Angle Between Two Tangents Drawn From That Point

The theorem is illustrated below. Proof: Construct the trianglesandby drawing radii as below. since both are radii of the circle andis common to both. Further, angle since these are between a tangent and a radius. From Pythagoras theorem,soand the triangles have three equal lengths so are congruent and angleandbisects

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Planes of Symmetry

A plane of symmetry cuts a shape in half so that on each side of the plane is a mirror image of the other side. Many shapes have planes of symmetry, including all prisms – shapes that have a constant cross section. This plane of symmetry of a prism is halfway along the prism, as […]

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Bearings

Bearings involve using trigonometry, generally the cosine or sine rules: Cosine Rule:  Sine Rule: For the above diagram, find a)The distance BC b)The bearing of A from B and the bearing of B from C. a)Label the triangle as above, with sides labelled by little letters opposite angles labelled by big letters. so b) We […]

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Transformations – Summary – Translations, Reflections, Rotations, Enlargements

The 4 basic transformations are illustrated above. Each translation movesin thedirection andin thedirection and is written  A rotation is defined by three things: clockwise or anticlockwise, the centre of rotation, written and the angle of rotation in degrees. A reflection is described by the line of reflection or the mirror line – we write down the […]

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