Circle theorems trip up more geometry students than almost any other topic — not because the ideas are deep, but because there are a dozen rules that look similar, and one wrong label unravels the whole problem. If you have a test coming up, a homework set full of angle-chasing questions, or a parent trying to explain why opposite angles in a cyclic quadrilateral add to 180°, this guide is built for you.

TLDR: Circle Theorems walks through every rule you actually need: the inscribed angle theorem and its cousins, tangent-chord angles, the alternate segment theorem, and the power of a point for chord and secant lengths. Each theorem is stated plainly, reasoned through briefly, and then applied in worked examples that mirror what shows up on geometry exams and standardized tests. The final section is a pure strategy guide for multi-step angle chasing — how to label a diagram, pick the right theorem, and chain results without losing the thread.

This is a short book by design. At roughly 15 pages, it covers exactly what a high school geometry student or early college math student needs and nothing more. No filler chapters, no review of material you already know. It works as a circle theorems study guide before an exam, a fast reference during a tutoring session, or a confidence-builder the night before class.

If circles have felt like a maze of half-remembered rules, this guide gives you the map. Grab it and get to work.

• Identify the parts of a circle (chord, arc, tangent, secant, inscribed and central angles) and use precise vocabulary.
• Apply the central angle, inscribed angle, and Thales' theorems to find unknown angles.
• Use chord, tangent, and secant length relationships (power of a point) to solve for unknown lengths.
• Recognize and use cyclic quadrilateral and tangent-chord angle properties.
• Combine multiple theorems in angle-chasing problems typical of geometry exams.

1. 1. Parts of a Circle: The Vocabulary You Need
   Defines radius, chord, arc, sector, tangent, secant, central and inscribed angles so the rest of the book has clear language.
2. 2. Angles in a Circle: The Inscribed Angle Theorem and Its Cousins
   Develops the central angle theorem, the inscribed angle theorem, Thales' theorem, and the angles-in-the-same-segment rule, with proofs sketched and worked examples.
3. 3. Cyclic Quadrilaterals and Tangent-Chord Angles
   Covers opposite angles of a cyclic quadrilateral summing to 180°, the exterior angle property, and the alternate segment (tangent-chord) theorem.
4. 4. Chords, Tangents, and Lengths: Power of a Point
   Treats the chord-chord, secant-secant, and tangent-secant length relationships as one idea (power of a point), plus the perpendicular-from-center-to-chord rule and equal tangents from an external point.
5. 5. Angle Chasing: Putting the Theorems Together
   A strategy guide for solving multi-step problems by labeling, identifying which theorem applies where, and chaining results, with two fully worked exam-style problems.