- Mathematics Advanced
- Year 10
Circle Geometry
approx. 7 hrs
5 topics
19 concepts
Build advanced deductive geometry skills in Circle Geometry and advance into Year 11 with confidence.
approx. 7 hrs
5 topics
19 concepts
Build advanced deductive geometry skills in Circle Geometry and advance into Year 11 with confidence.
Year 10 Circle Geometry reveals important theorems about the circle and aligns with the Measurement and Geometry Strand of the Australian curriculum. In this learning program, students develop an understanding of each circle theorem and confidently select and apply this theory to support geometrical proofs.
This learning program is made up of the following 5 topics, broken down into 19 concepts.
Use terminology associated with angles in circles
When two circles intersect, the line joining their centres bisects their common chord at right angles
A line through the centre of a circle perpendicular to a chord bisects the chord, and conversely
Equal chords subtend equal angles at the centre and conversely
Equal arcs subtend equal angles at the circumference, and conversely
The angle at the centre is twice the angle at the circumference standing on the same arc
The angle at the circumference in a semi-circle is 90°, and conversely
Proving Concyclicity
The opposite angles of a cyclic quadrilateral are supplementary, and conversely
The exterior angle of a cyclic quadrilateral equals the interior opposite (or remote) angle, and conversely
The line joining the centers of two circles passes through their point of contact
A radius (diameter) of a circle is perpendicular to the tangent at their point of contact
The products of the intercepts of intersecting secants are equal
The products of the intercepts of two intersecting chords are equal, and conversely
Tangents from an external point are equal.
The angle between a tangent and a chord equals the angle at the circumference in the alternate segment
The Tangent-Secant Theorem
Apply tangent and secant properties of circles to find unknown angles and lengths
Find unknown angles and lengths using chord and angle properties
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