• 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.

Available in


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.

Topics & Concepts We Cover

This learning program is made up of the following 5 topics, broken down into 19 concepts.

  • Circle Definitions 1 concept

    1. Use terminology associated with angles in circles

  • Chord Properties 3 concepts

    1. When two circles intersect, the line joining their centres bisects their common chord at right angles

    2. A line through the centre of a circle perpendicular to a chord bisects the chord, and conversely

    3. Equal chords subtend equal angles at the centre and conversely

  • Angle Properties 6 concepts

    1. The angle at the centre is twice the angle at the circumference standing on the same arc

    2. The angle at the circumference in a semi-circle is 90°, and conversely

    3. Equal arcs subtend equal angles at the circumference, and conversely

    4. The exterior angle of a cyclic quadrilateral equals the interior opposite (or remote) angle, and conversely

    5. The opposite angles of a cyclic quadrilateral are supplementary, and conversely

    6. Proving Concyclicity

  • Tangent and Secant Properties 7 concepts

    1. The products of the intercepts of two intersecting chords are equal, and conversely

    2. The line joining the centers of two circles passes through their point of contact

    3. A radius (diameter) of a circle is perpendicular to the tangent at their point of contact

    4. The products of the intercepts of intersecting secants are equal

    5. The angle between a tangent and a chord equals the angle at the circumference in the alternate segment

    6. The Tangent-Secant Theorem

    7. Tangents from an external point are equal.

  • Problems using Circle Theorems 2 concepts

    1. Find unknown angles and lengths using chord and angle properties

    2. Apply tangent and secant properties of circles to find unknown angles and lengths

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Circle Geometry


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

Ready to start this program?

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Starting at

$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime

Access to practice questions

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