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Circle Theorem Rules with Examples [Questions & Common Mistakes Included]

09 Aug 2022

13 minutes

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Can you score A+ in the maths assignment? Most of the students would answer NO! It is because they have to face countless issues while writing this assignment. Different UK students face various problems, but some of the problems remain the same for all the students. Generally, they get stuck when they solve the circle theorem questions. It can happen because the students face difficulties in understanding the circle theorem rules effectively. The UK students have to deal with the circle theorem questions in which they have to prove the theorems. These are the most time taking and confusing ones. The students don’t practice enough questions, and due to this, they fail to solve them.

Well! The reasons can be anything, but the students have to submit a polished paper on time anyhow. If you have the circle theorem assignment and are worried about how to solve the circle theorem questions without any mistake, then this blog can prove helpful. Before you jump to solve the questions, must know some terms related to the circle theorem. Move ahead to know them!

### Must-Know Terms to Understand the Circle Theorem Rules

1. Radius: Radius is a distance from the center to the edge of the circle.

Formula:r= c/2π

1. Diameter: It is a line drawn from one edge of the circle to another, and it passes through the center.

Formula: d=2r

1. Chord: When both endpoints of a line lie on the edge of the circle, it is called a chord.

Formula:Length of chord = 2√ (r2– d2)

1. Segment: It is an area in the circle and bounded by the chords.

Formula:Area of a Segment in Radians A = (½) × r2(θ – Sin θ)

1. Circumference: It is also called a perimeter. The total boundary of the circle is covered in it.

Formula:C= 2πr

1. Tangent: Tangent is perpendicular to the circle, and it touches one point of it.

Formula: Y=m x+c

1. Arc: It is any portion of the circumference of the circle.

Formula:Arc length = 2πr (θ/360)

1. Sector: A sector is a portion enclosed within the two radii of the circle.

Formula:Area of sector = (θ/360°) × πr2

### What Are the Types of Circle Theorems?

Angles Formed at the Centre and Circumference

Explanation: An angle at the center is always twice the angle at the circumference. CAB= 2CDB.

Angle in a Semicircle

Explanation: Angle in a semicircle is the right angle. Here, APB is 90°.

Angles in the Same Segment

Explanation: Angles in the same segment are always equal. In this diagram, BCE=BDE

Explanation: Opposite angles in a cyclic quadrilateral add up to 180°. Here, CFE+CDE= 180°.

Length of Tangents

Explanation: >The length of the two tangents is equal in a circle if they are drawn from one point of the circle. Here, DC = EC.

Angle Between Circle Tangent and Radius

Explanation: The angle between a tangent and a radius in a circle is the right angle. Hence, ODC= 90° and OEC= 90°.

Alternate Segment Theorem

Explanation: The angle between tangent and chord on the point (here, D) is equal to the angle in the alternate segment. As a result, ABC=CAP.

The Perpendicular from the Centre of the Circle Bisects the Chord

Explanation: Perpendicular line from the center (O) cuts the chord (CD) at the center. So, the perpendicular from the center bisects the chord. So, DBO = 90° and CBO = 90°.

### Easy Ways to Understand the Circle Theorem Rules!

• Start from the basics of the circle and understand all the aspects. It will help you to understand the circle theorem rules.
• Practice drawing the diagrams; this will make the terms related to the circle more clear.
• Make a list of all the terms related to the circle theorem; see their diagrams properly and try to draw them on your own.
• Don’t mug up the formulas; instead, understand them with the help of diagrams and different ways.
• For more clarity of the concepts, change the variables. Give them different names, and then practice the questions.
• Watch the videos, as visual experience can make things clearer for you.
• Try to follow the above ways to understand the circle theorem rules easily. If you want to know what types of questions are asked in the circle theorem assignment, then know the 7 best questions below.

### 5 Best Questions to Practice the Circle Theorem

Question 1. ABC are the points on the circumference, and O is the center of the circle. Angle A = 29°. You have to find the value of angle B.

Question 2. A, B, and C are the points on the circumference of the circle, and O is the center point of the circle. Angle AOB is 112°. You have to find the size of angle ACB.

Question 3. A, B, C, and D are the three points on the circumference of the circle. On the basis of this, answer the below two questions.

• Angle DAB Size=? (b) Angle ABC Size=?

Question 4. Provide the answer to the below questions.

(a) Calculate the size of angle x.

(b) Support the answer with a reason.

Question 5. A, B, C, and D are three points on the circumference of a circle, and the center is O; AC is a diameter.

Angle ABD = 58°

Angle CDB = 22°

You have to find the sizes of angle ACD and ACB, with reasons for your answers.

These all 5 questions are vital. So read them effectively and then try to find their answers. You can find out the answers quickly if you know the circle theorem rules. UK students have to solve these types of questions in their assignments. Often, you have to prove the answer with reasons. GCSE students also have to solve circle theorem questions in their maths papers.

Many UK students get stuck when they try to solve the circle theorem questions and make mistakes. If you want to know what mistakes students make while writing the maths assignments, then read below. This is because you can also make such types of mistakes.

### 5 Mistakes Students Make in the Circle Theorem Assignment!

1. Avoiding Planning: Without any planning, you can’t make the assignment impressive. Often, the questions are so tricky that you can’t understand how to solve and find their answers. If you plan, then you can solve the questions properly.
1. Practicing Only One Type of Questions: Most of the time, you fail to write an impeccable assignment because you practice only one type of question. To deal with them perfectly, you must focus on all the types of questions. Make a checklist; as you finish practicing one type of question, then mark it and move to the next type.
1. Not Focusing on the Basics: Circle theorems questions can be solved effectively, and you can avoid the silly mistakes if your basics are strong. Many students don’t focus on the basics, and then they face issues while solving the questions. If you have a calculus assignment, then also you must know the basics of the circle theorem.
1. Use of the Short Tricks: If you use the short tricks without knowing the basics, then you can make several mistakes. Short- tricks can work when you know the concepts effectively. Many times, you see that circle theorem questions with solutions are solved by using the short tricks. But whenever you see such types of answers, cross-check to know whether they are correct or not.
1. Lack of Analytical Skills: You have to deal with proof-based questions as well. In these types of questions, you can make several mistakes if you don’t analyze them. Lack of understanding of the circle theorem rules causes major problems.

Focus on the above-mentioned mistakes and eliminate them from your paper. If you can’t deal with the mistakes effectively, then also don’t worry. Online assignment help providers can offer you an error-free circle theorem assignment. If you don’t know which website offers the best writing help, then you must read below.

### Who Can Help Me in Writing Circle Theorem Assignment?

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Maths assignments are generally time taking; that is why most students give up on them. Focus on the above mistakes while writing to reduce the chances of errors. If you still get stuck while writing and face difficulty in understanding the circle theorem rules, then take the best writing assistance and secure the highest grade.