Dive into a comprehensive 6-hour tutorial on Circle Geometry presented by Eddie Woo. Explore fundamental concepts such as finding the center of a circle passing through three points, tangent and radius perpendicularity, and components of a circle. Master angle properties, cyclic quadrilateral characteristics, and the Angle in the Alternate Segment Theorem. Tackle challenging HSC-level questions, covering topics like similar triangles and radius calculations. Examine chord properties, tangent characteristics, and intercept properties through detailed proofs and examples. Investigate congruent triangles in circles, opposite angles in cyclic quadrilaterals, and complex scenarios involving overlapping circles and collinear points. Conclude with an in-depth study of circle tangents, their properties, and practical applications in geometric proofs.
Overview
Syllabus
Finding the Centre of a Circle Passing Through 3 Points.
Tangent & Radius are Perpendicular (Demonstration Through Secants).
Components of a Circle.
Angle Properties in a Circle.
Cyclic Quadrilateral Properties.
Angle in the Alternate Segment Theorem.
Circle Geometry Question (Using Theorem Converses).
HSC Wk6 Quiz Overview (Solving A Harder Circle Geometry Question).
HSC Circle Geometry Question (1 of 3: Similar Triangles).
HSC Circle Geometry Question (2 of 3: Intermediate Length).
HSC Circle Geometry Question (3 of 3: Finding Radius).
Chord Properties (Circle Geometry).
Components of a Circle.
Angle Properties - Circle Geometry (Angle at the centre/circumference).
Angle Properties - Circle Geometry (Angle in a semicircle).
Angle Properties - Circle Geometry (Second proof of angle at the centre/circumference).
Angle Properties - Circle Geometry (Angles in the same segment).
Tangent Properties - Circle Geometry (Tangent is perpendicular to radius).
Tangent Properties - Circle Geometry (Tangents from an external point are equal).
Angle in the Alternate Segment - Circle Geometry (1 of 3: Setup).
Angle in the Alternate Segment - Circle Geometry (2 of 3: Proof).
Angle in the Alternate Segment - Circle Geometry (3 of 3: Conclusion and overall summary).
Intercept Properties - Circle Geometry (1 of 3: Intersecting chords).
Intercept Properties - Circle Geometry (2 of 3: Secants from a point).
Intercept Properties - Circle Geometry (3 of 3: Tangent & secant).
Tough Circle Geometry Question (1 of 3: Finding & using congruent triangles).
Tough Circle Geometry Question (2 of 3: Proving a given chord is a diameter).
Tough Circle Geometry Question (3 of 3: Using tangent properties).
Congruent Triangles in Circles (1 of 2: Equal chords).
Congruent Triangles in Circles (2 of 2: Chord bisector).
Opposite Angles in a Cyclic Quadrilateral (1 of 2: Introduction).
Opposite Angles in a Cyclic Quadrilateral (2 of 2: Completing the proof).
Tough Circle Geometry Question (1 of 2: Set up & initial arguments).
Tough Circle Geometry Question (2 of 2: Proving points collinear).
Equal Overlapping Circles Question (1 of 2: Identifying congruent triangles).
Equal Overlapping Circles Question (2 of 2: Finding equal lengths).
Tangents of Circles (1 of 4: What are they?).
Tangents of Circles (2 of 4: Tangent perpendicular to radius).
Tangents of Circles (3 of 4: Tangents from an external point).
Tangents of Circles (4 of 4: Angle in the alternate segment).
Proof: Centres & point of contact are collinear on touching circles.
Circle Geometry Proof - Triangles & Tangents.
Circle Geometry Proof (Touching circles with a second common tangent).
Circle Geometry Example Question (worked proof).
Taught by
Eddie Woo
