Circle Theorem - Resource Pack

Lesson Contents: Circle Theorems

Download Includes:

• A comprehensive PowerPoint lesson designed for interactive use with a clicker, mouse, or keyboard to navigate through animations and display fully animated and worked solutions.

Topic of Study: Circle Theorems

Differentiated Objectives:

1. Developing Learners will be able to:

   • Apply circle theorems to find missing angles.

2. Secure Learners will be able to:

   • Justify, with reason, the circle theorems they apply to find missing angles.

3. Excelling Learners will be able to:

   • Solve unfamiliar problems using circle theorems.

Main Components:

The main segment of the lesson unfolds with a step-by-step approach:

• Walked through examples demonstrate the application of circle theorems.
• Practice questions on accompanying worksheets progress from basic queries on the just-introduced theorem to exam-style questions utilizing each of the theorems previously introduced.
• All solutions are provided directly within the PowerPoint presentation for easy reference.

Circle Theorem Statements:

1. Angles in the Same Segment:

   • Angles in the same segment of a circle are equal.

2. Opposite Angles in a Cyclic Quadrilateral:

   • Opposite angles in a cyclic quadrilateral add up to 180 degrees.

3. Angle at the Center:

   • The angle at the center of a circle is twice any angle at the circumference subtended by the same arc.

4. Angles in a Semi-Circle:

   • Angles formed in a semi-circle are always right angles.

5. Alternate Segment Theorem:

   • An angle between a chord and a tangent is equal to the angle in the alternate segment.

6. Tangent-Radius Perpendicularity:

   • A radius at the point of tangency to a circle is perpendicular to the tangent.

7. *Cyclic Quadrilateral Diagonals:

   • The diagonals of a cyclic quadrilateral bisect each other at right angles.

8. Chord Bisection:

   • A chord that passes through the center of a circle is bisected by the circle into two equal parts.

This lesson is structured to empower learners at various levels, ensuring a comprehensive understanding of circle theorems and proficiency in their application across different scenarios.