Tec — The Education Consultancy

Topics covered

• Terminology — sector, segment (major/minor), angle in a segment (inscribed angle), and central angle of an arc
• Theorem 28.1 — the central angle of a minor arc is double the inscribed angle of the corresponding major arc, with its corollaries
• Theorem 28.2 — any two angles in the same segment of a circle are equal
• Theorem 28.3 — the angle in a semicircle is a right angle; in a major segment it is acute; in a minor segment it is obtuse
• Theorem 28.4 — the opposite angles of a cyclic quadrilateral are supplementary, with the parallelogram-inscribed-in-a-circle corollary
• Applying these theorems together to solve numerical problems involving diameters, chords, and inscribed quadrilaterals
• Proving results such as a rhombus inscribed in a circle is a square, and the exterior angle of a cyclic quadrilateral equals the interior opposite angle