Mastering the concepts of circles is crucial in geometry, and this article aims to break down the various concepts into manageable steps. 

From foundational definitions such as angle properties of circles, to advanced topics such as tangents and sector areas, each section is crafted to enhance your understanding and proficiency in handling circle-related questions. You will also find a series of practice questions designed to reinforce your understanding. Each question is meticulously crafted by our teachers to challenge and expand your knowledge, ensuring that you’re fully prepared to tackle circle-related questions in your exams!

Before we dive into the different concepts, take a moment to review this video to briefly recap on the different types of theorems!


Angle Properties of Circles

In this section, we will explore the angle properties of circles so as to understand their geometric configurations.




Chord Properties of Circles

In this section, we’ll explore how chords interact with circles, discovering their relationships with diameters, radii, and central angles. 

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Tangent Properties of Circles

In this section, we will explore how circles relate to tangents, diameters, radii, and central angles.


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Exploring the Alternate Segment Theorem

The Alternate Segment Theorem, also referred to as the Tangent-Chord Theorem, states that if line XY is tangent to a circle at point A, then the angles formed at points B and C by extending the tangent to intersect the circle at points B and C respectively, are equal to the angles subtended by the chord XY. 

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In other words, ∠XAB = ∠ACB and ∠YAC = ∠ABC


Checkpoint! Answer the following question on circles.

Based on the following diagrams, select the option that correctly illustrates the Alternate Segment Theorem.



Check your Answers! Did you get it right?

The answer is option 3.


Proof Techniques for Circles

In this section, you will find typical exam questions. Your task will be to provide proofs for the following questions by applying the concepts and techniques that you have learned in the above sections regarding the different properties of circles

Let’s work through the first question together!

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Now, you give it a try!


Checkpoint! Answer the following questions below.

Circles Q1


Check your Answers! Did you get it right?

Circles Ans


Test your Understanding

Mastering these concepts related to circles requires diligent practice and understanding of geometric principles. The following exercises are designed to reinforce your knowledge of circle properties, including angles, chords, tangents, and the relationships between these elements. 

Remember, consistent practice is key to gaining confidence and proficiency in solving circle-related problems. Let’s delve into these questions to sharpen your skills and deepen your understanding.


Question 1:



Check your Answers! Did you get Question 1 right?

Question 2:

Circles P2


Check your Answers! Did you get Question 2 right?



Question 3:

Circles P3


Check your Answers! Did you get Question 3 right?

Circles P3

Want to learn more? 

Still want more? Then, join our interactive live teaching sessions, where we explore various topics covered in the GCE O Level Elementary and Advanced Mathematics exams, including interesting subjects like circles and more.

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