# IGCSE Mathematics: Intersecting Chords

Intersecting chords can be a challenging topic for many students, often leading to common mistakes such as misunderstanding the properties of similar triangles and incorrectly applying the intersecting chords theorem. These mistakes often stem from a lack of understanding of the geometric principles involved. The tutorials and planned lesson address these mistakes by providing clear, step-by-step explanations and visual aids that help students grasp the underlying concepts.

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Members of Mr Mathematics can download the full lesson and additional student worksheet. These resources ensure a thorough understanding of the topics covered and provide ample opportunities for students to apply what they’ve learned.

## Part 1: Introduction to Intersecting Chords

Key Skills Learned:

• Proving triangle similarity using angle properties.
• Derivation of the intersecting chord property.

Watch Part 1 of the Tutorial

The first part of the lesson introduces the concept of intersecting chords. I demonstrate how triangles APC and BPD are similar by using the circle theorem angles in the same segment . This part lays the foundation for understanding how the intersecting chords theorem works.

## Part 2: Solving Problems Using Derived Formulas

Key Skills Learned:

• Applying the intersecting chords theorem to solve for unknown lengths.
• Practicing with multiple problem scenarios.

Watch Part 2 of the Tutorial

In the second part, the lesson progresses to solving problems using the formula derived from the intersecting chords theorem,

 AP \times PB = CP \times PD

This part focuses on applying the theorem to various problems, reinforcing the concept through practice.

## Part 3: Exam Style Question

Key Skills Learned:

• Solving complex problems involving intersecting chords.
• Link to trigonometry and solving problems with non-right-angled triangles.

Watch Part 3 of the Tutorial

The final part of the lesson challenges students with an exam-style question. This section aims to consolidate and assess the students’ understanding and ability to apply the intersecting chords theorem.

Exclusive Membership Benefits

As a member of Mr Mathematics, you gain access to comprehensive lesson plans and student handouts that accompany each tutorial. These resources include:

Full Lesson Plans: Structured PowerPoint presentations with starter, main, and plenary sections.

Differentiated Worksheets: Additional practice problems tailored to various skill levels, ensuring all students can effectively learn and apply the concepts.

Detailed Solutions: Step-by-step solutions to reinforce understanding and support self-assessment.

By joining Mr Mathematics, you not only enhance your learning experience but also ensure consistent practice and mastery of A-Level Mathematics concepts.

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