Become A Master of Geometry - Circles

High school math that covers Geometry - Circles in detail, with a step-by-step approach with Theorems and proofs.

Created byLakshmi Narayana

Last updated 11/2022

English

What you'll learn

Introduction to Circles – Chord, Arc, Semi-circle, Circumference, Segment, Sector, Secant of a Circle.
Tangent to a Circle and Proofs.
Number of Tangents from a Point on a Circle and Their Length.
Properties of Tangents, Secant and Intersecting Lines.
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

6 sections • 37 lectures • 3h 37m total length

Introduction11:23
Introduction
Theorem 15:28
The TANGENT at any point of a circle is perpendicular to the radius through the point of contact.
Q 13:05
From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.
Q 23:37
In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
Test your understanding
Home Assignment

Introduction6:53
Number of Tangents from a Point on a Circle
Theorem 23:35
The lengths of two tangents drawn from an external point to a circle are equal.
Q 13:00
Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Q 26:04
In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then find the radius of the smaller circle.
Q 33:59
Two concentric circles are of radii 7 cm and r cm respectively where r > 7. A chord of the larger circle of the length 48 cm, touches the smaller circle. Find the value of r.
Q 47:12
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Figure). Find the length TP.
Test your understanding
Home Assignment

Introduction2:44
Number of Tangents from a Point on a Circle
Q 18:06
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ.
Q 25:33
If PA and PB are tangents from an outside point P. such that PA = 10 cm and ∠APB = 60°. Find the length of chord AB.
Q 33:33
If two tangents inclined at an angle of 60° are drawn to a circle of a radius 3 cm, then find the length of each tangent.
Q 44:38
In two concentric circles, prove that all chord of the outer circle which touch the inner circle are of equal length.
Test your understanding
Home Assignment

Introduction2:27
Miscellaneous problems related to circles.
Q 18:29
In fig. the radius of the in circle of △ABC of area 84 cm2 and the lengths of the segments AP and BP into which side AB is divided by the point of contact are 6 cm and 8 cm. Find the lengths of the sides AC and BC.
Q 27:10
If a, b and c are the sides of a right angled triangle, where c is hypotenuse, then prove that the radius of the circle which touches the sides of the triangle is given by r = (a+b-c)/2
Q 35:30
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA.
Q 46:48
In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, P and S respectively. If AB = 29 cm, AD = 23 cm, ZB = 90° and DS = 5 cm, then find the radius of the circle (in cm.).
Test your understanding
Home Assignment

Q 11:20
How many tangents can a circle have?
Q 22:32
Fill in the blanks :
(i) A tangent to a circle intersects it in ___________ point (s).
(ii) A line intersecting a circle in two points is called a _____________.
(iii) A circle can have ___________ parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called __________.
Q 33:19
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
(A) 12 cm (B) 13 cm (C) 8.5 cm (D) cm.
Q 41:44
Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

Q 14:41
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
(A) 7 cm (B) 12 cm
(C) 15 cm (D) 24.5 cm
Q 23:17
In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that
POQ = 110°, then PTQ is equal to
(A) 60° (B) 70° (C) 80° (D) 90°
Q 39:10
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then POA is equal to
(A) 50° (B) 60° (C) 70° (D) 80°
Q 46:03
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Q 57:16
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Q 64:59
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Q 77:03
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Q 87:17
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC
Q 910:15
XY and X’Y’ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that AOB = 90°.
Q 105:34
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Q 116:57
Prove that the parallelogram circumscribing a circle is a rhombus.
Q 1217:00
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
Q 139:40
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Requirements

Elementary knowledge of basic Geometry.
Each chapter is inbuilt with prerequisite knowledge classes where the child gets immense knowledge and a clear understanding of the chapters.

Description

This course is intended for students under 18 may use the services only if a parent or guardian opens their account, handles any enrollments, and manages their account usage.
This course is carefully designed to explain various applications of Geometry - Circles .
It has 37 lectures spanning around three and half hours of on-demand videos that are divided into 4 sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key. The students are encouraged to solve practice questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand very well.
It covers 100% video solutions of the NCERT exercises , with selected NCERT exemplars and R D Sharma.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in math. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning maths and never feel that maths is troublesome.

Topics covered in the course:

Review of Concepts Circles and related terms.
Introduction to Circles – Chord, Arc, Semi-circle, Circumference, Segment, Sector, Secant of a Circle.
Tangent to a Circle.
Number of Tangents from a Point on a Circle and Their Length.
Properties of Tangents, Secant and Intersecting Lines.
Solving different real-life situations by using Circles.

With this course you'll also get:

Perfect your mathematical skills on Geometry – Circles.
A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the real number systems.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of the chapter and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Anyone who wants to proficient mathematics and the solving different real life situations on Geometry - Circles well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.

Become A Master of Geometry - Circles

What you'll learn

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Course content

Session 14 lectures • 24min

Session 26 lectures • 31min

Session 35 lectures • 25min

Session 45 lectures • 30min

Exercise 10.14 lectures • 9min

Exercise 10.213 lectures • 1hr 39min

Requirements

Description

Who this course is for: