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Learn Cyclic quadrilaterals

All About Cyclic Quadrilaterals video thumbnail

All About Cyclic Quadrilaterals

In the Class 9 Mathematics curriculum, the "Circles" chapter introduces several fascinating geometric concepts, one of the most important being the cyclic quadrilateral. Imagine a four-sided polygon, but with a special condition: all four of its vertices (corners) must lie perfectly on the boundary (circumference) of a single circle. When a quadrilateral is inscribed inside a circle in this manner, it is known as a cyclic quadrilateral. Understanding this specific shape is crucial because it unlocks unique angle properties that regular quadrilaterals do not possess, forming the essential foundation for complex geometric proofs in higher geometry.

The core mathematical logic of a cyclic quadrilateral revolves around the relationship between its opposite angles. The foundational theorem states that the sum of either pair of opposite angles of a cyclic quadrilateral is exactly 180°. If we have a cyclic quadrilateral ABCD, this means mathematically that ∠A + ∠C = 180° and ∠B + ∠D = 180°. Because these opposite angles add up to a straight line, they are supplementary. The converse is also strictly true: if the opposite angles of any given quadrilateral sum up to 180°, then that quadrilateral must be cyclic. Another crucial property to remember for problem-solving is that if one side of a cyclic quadrilateral is produced (extended outward), the exterior angle formed is exactly equal to the interior opposite angle.

Properties of a Cyclic Quadrilateral A B C D E Theorem 1: Opposite Angles ∠A + ∠C = 180° (Red dot + Blue dot are supplementary) ∠B + ∠D = 180° (Green dot + Purple dot are supplementary) Theorem 2: Exterior Angle Exterior ∠BCE = Interior ∠A (Notice the matching Red dots)

Looking at the diagram above, you can see a cyclic quadrilateral ABCD correctly inscribed inside a dashed circle. Notice how all four vertices—A, B, C, and D—touch the circle's boundary exactly. The visual uses distinct colored dots to help you grasp the theorems clearly. For Theorem 1, the opposite angles form supplementary pairs: Angle A (red dot) and Angle C (blue dot) sum up to 180°, just as Angle B and Angle D do. Furthermore, if you look at vertex C, the bottom side DC has been extended outward to a point E. This creates the exterior angle labeled ∠BCE. According to Theorem 2, this exterior angle—marked with a red dot—is perfectly equal in measure to the interior opposite angle at vertex A, which strategically shares the matching red dot. In your CBSE Class 9 exams, these exact properties are heavily tested. You will often be given the measure of just one or two angles and asked to logically deduce the rest using these relationships.

Mastering geometry concepts like cyclic quadrilaterals requires practice and sometimes a bit of expert guided help. If you find visualizing these circle theorems or solving complex angle proofs challenging, UrbanPro is here to support your learning journey. On UrbanPro, you can easily connect with highly experienced and verified Class 9 Mathematics tutors who specialize in making CBSE geometry simple, engaging, and intuitive. Whether you prefer personalized one-on-one online tuition or local offline classes, UrbanPro offers a trusted platform to find the perfect tutor to boost your conceptual clarity and maximize your exam scores.


Other Concepts in Circles


Other Concept Videos for Cyclic quadrilaterals

All About Cyclic Quadrilaterals video thumbnail

All About Cyclic Quadrilaterals

CBSE - Class 9>Mathematics>Circles>Cyclic quadrilaterals


All About Cyclic Quadrilaterals video thumbnail

All About Cyclic Quadrilaterals

CBSE - Class 9>Mathematics>Circles>Cyclic quadrilaterals

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Top Tutors who teach Cyclic quadrilaterals

(68)
superTutorSuper Tutor
locationImg Sector 92, Gurgaon
20 yrs of Exp 20 students
greenClock 1281 hrs of classes completed
rsIcon 800 per hour
Teaching mathematics since last 20 years. Doing research on Vedic mathematics
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

Teaching since last 20 years

Nandini Mishra

Amit ji is a fantastic teacher. My daughter is very happy with her studies. He is exactly what she needed, a teacher with deep understanding of his subject and a very good communicator. If there is one gripe that I may mention, it's time. We would love to have more classes to cover Physics, but he is completely booked for his time. I would highly recommend him. Thank you.

Skills: Mathematics , Physics and more
Also teaches: Class 11 Tuition, Soft Skills Training and more

Avishake Chatterjee Class 9 Tuition trainer in Kolkata
(62)
superTutorSuper Tutor
locationImg Behala, Kolkata
8 yrs of Exp 7 students
greenClock 947 hrs of classes completed
rsIcon 700 per hour
MATHS EXPERT having an experience of 6+years
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

As a passionate mathematics teacher, I have always enjoyed imparting knowledge to others. I am a B.Tech graduate in Electronics and Communication. I have been teaching mathematics for over four years, and my love for the subject has grown stronger with time. I started teaching as a part-time tutor while pursuing my engineering degree and fell in love with the profession. After completing my degree, I worked with Byjus, one of the leading Edtech companies in India, as a mathematics teacher for two years. While I enjoyed my time at Byju's, I could do more as a teacher and wanted to explore new avenues. I joined Vedantu, an online learning platform, where I have been teaching mathematics for the last two years. I started my journey as a math teacher out of pure passion. Mathematics has always been my favourite subject, and I enjoyed solving problems and equations from a young age. As I grew older, I realised I had a natural talent for teaching, and I decided to pursue it as a career. Currently, I provide mathematics classes for students from sixth to twelfth for all boards, including ICSE, CBSE, and West Bengal. I teach offline and online classes, each lasting for one and a half hours. I use interactive tools such as Zoom, Pentab, and One Note to make my lessons engaging and interactive for my students. To help my students excel in mathematics, I provide them with reference books, notes, and in-built assignments to test their knowledge. I also conduct monthly tests to assess their progress and identify improvement areas. Teaching on UrbanPro has allowed me to interact with students from different parts of the country and help them realise their full potential in mathematics. I want to continue making a positive impact in the lives of my students and help them develop a love for mathematics, just like I did

Aaa Mukherjee

Avishake Sir is an exceptional maths teacher! Engaging, patient, and effective. He break down complex concepts into easy-to-understand bits , provide individual attention and boost confidence. Highly recommended!"

Skills: Mathematics
Also teaches: Class 7 Tuition, Class 6 Tuition and more

Sai V. Class 9 Tuition trainer in Madappanahalli
(141)
superTutorSuper Tutor
locationImg Itagalpura Main Rd, Madappanahalli
17 yrs of Exp 43 students
greenClock 3517 hrs of classes completed
rsIcon 400 per hour
MSc, BEd , (Phd), Member of Royal Society UK
Online Classes Online Classes

I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classes IX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.

Skills: Mathematics , Physics and more
Also teaches: Engineering Entrance Coaching, Parenting and more

(59)
superTutorSuper Tutor
locationImg Sector 5, Dwarka, Delhi
10 yrs of Exp 33 students
greenClock 1162 hrs of classes completed
rsIcon 500 per hour
10 Yrs in Teaching, Conduct Batch Of Two Kids, One-to-One classes. ShortTermPrep & LongTermClasses.
Online Classes Online Classes

I teach Math and Science to 8th-12th standard students and have been teaching for more than 10 years. Batch of 2 Students: I conduct these small batches with a pair of students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). Works for those students/parents who are looking for individual attention for their kids but still want it to be a little affordable. *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 4500/- per month/12 classes. Batch of 6 Students: I conduct these small batches with 5-6 students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). *4 classes per week (So 16 a month) *Maths and Science *Fee Rs. 4000/- per month/16 classes. I will start the classes immediately once the first kid enrolls. ------------------------------------------------------------------------------- Individual/Private/One-to-One classes: I conduct these one to one classes for those students willing to have one to one setup (I cover all popular boards CBSE, ICSE, IGCSE etc.). *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 7000/- per month/12 classes. ------------------------------------------------------------------------------- I took classes and batches in different institutions.

Surabhi rai

The teacher is very good. He understands the students strength and weakness and decides the pace of learning. He also tries to make the student comfortable and at ease with his/her capacity and then works on the child. It is not just Math he works on but the child's confidence and comfort with the subject. Highly recommended.

Skills: Mathematics , Physics and more
Also teaches: Spoken English, Python Training and more

(26)
superTutorSuper Tutor
locationImg Rohini Sector-24, Delhi
20 yrs of Exp 10 students
greenClock 1404 hrs of classes completed
rsIcon 450 per hour
Experienced Maths teacher with more than 20 years of experience.
Online Classes Online Classes

I am a teacher and I have been teaching for the past 20 years. l am presently teaching in a school. l have done MSc in Maths and have taught many students.

Amit Kumar

Thanks Ma'am for supporting Anvi in the subject. She has been getting more comfortable and relaxed with the theory and concepts in mathematics. Her fear is waning away and she shows an increased interest in the subject. I will definitely recommend you to all prospective parents. Thanks again!

Skills: Mathematics , Physics and more
Also teaches: Class 8 Tuition, Class 12 Tuition and more

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Other Subjects in CBSE - Class 9


FAQ

What is the meaning of Cyclic quadrilaterals?

It refers to a specific mathematical method or property in Circles used to solve problems involving Cyclic quadrilaterals.

Why is Cyclic quadrilaterals important for CBSE - Class 9 exams?

This concept is crucial for the exams as questions related to Circles and specifically Cyclic quadrilaterals are very common. It helps secure marks in the section effectively.

Is Cyclic quadrilaterals part of the latest NCERT syllabus?

Yes, Cyclic quadrilaterals is an integral part of the CBSE - Class 9 NCERT Mathematics syllabus. It is a key topic covered in the Circles chapter.

What are common mistakes students make with Cyclic quadrilaterals?

Students often miss the minute details or fundamental definitions of Cyclic quadrilaterals. Regular revision and practice are needed to master the nuances.

How should I approach learning Cyclic quadrilaterals?

Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.

How can UrbanPro help me understand Cyclic quadrilaterals better?

UrbanPro connects you with experienced Mathematics tutors who can explain Cyclic quadrilaterals with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.

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