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Lesson

Alternate Segment Theorem

The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle opposite to the chord in the alternate segment. This means if a tangent touches a circle at point A and AB is a chord, then the angle between the tangent and chord equals the angle in the opposite side of the circle.

40min lesson

Objectives3 goals Lesson5 blocks Review2 assets Practice32 items

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Understand alternate segment theorem in the Circles chapter.
Connect the idea with formulas, examples, and exam-style questions.
Use flashcards, notes, MCQs, and LAQs to check readiness.

Lesson

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5 sections

Example

Determining an Angle Subtended by a Diameter

In a circle with diameter AB, point C lies on the circumference such that angle ACB is 90 degrees. If BC = 8 cm and CA = 6 cm, find the length of AB. 1. Since AB is a diameter, ∠ACB = 90° by the angle-in-a-semicircle theorem. 2. So triangle ABC is right-angled at C. 3. Apply Pythagoras theorem: AB² = AC² + BC² = 6² + 8² = 36 + 64 = 100. 4. Therefore, AB = √100 = 10 cm. Final answer: AB = 10 cm Exam tip: Remember, any angle subtended by a diameter in a semicircle is always 90 degrees. Common mistake: Incorrectly applying the Pythagorean theorem.

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5 lesson sections1 cards / 1 notes18 MCQs / 14 written questions

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Alternate Segment Theorem

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32 prompts

18 MCQs14 LAQsMixed test

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Circles

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Alternate Segment Theorem

What to understand

Step-by-step lesson

Determining an Angle Subtended by a Diameter

Finding an Angle Subtended by a Diameter

Finding the Angle Subtended by a Diameter at Any Point on the Circumference