# Geometry: Circle | Class 10 Mathematics Solutions

## Unit: 15  Geometry: Circle

Before starting the discussion about Geometry: Circle we have to review the following concept.

Well, a geometrical path traced out by a moving point in a plane such that its distance from some fixed point always remains equal or constant is called a circle. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle. The outer path is called the circumference.

A circle can also be defined as a closed plane figure bounded by a curve such that every point of the curve remains equidistant from a fixed point. The fixed point is called the centre of the circle, the constant distance is called the radius of the circle and the bounding curve is called the circumference of the circle.

### Some definitions

#### Chord

A line segment joining any two points of the circumference is called the chord of a circle.

#### Diameter

The longest chord passing through the centre of a circle is called its diameter. It is twice the radius of the circle.

#### Semicircle

One of two parts of a circle made by its diameter is said to be a semi-circle.

#### Segments

Two unequal parts of a circle made by a chord are called its segments. The larger one is called major segment and the smaller one is called minor segment.

#### Sector

The area of a circle between any two radii is called its sector. The greater one is called major sector and the smaller one is called minor sector.

#### Central angle

The angle subtended by an arc at the centre of a circle is called its central angle. It is the angle made by any two radii of the circle at its centre. The central angle and its opposite arc are equal in degree measure.

#### Arc

A part of the circumference of a circle is called an arc.

#### Inscribed angle

An angle subtended by an arc of a circle at its circumference is called an inscribed angle. An inscribed angle is an angle made by any two chords of a circle at its circumference. The inscribed angle is also called an angle at the circumference.

#### Concentric circles

Two or more than two circles having same centre are called concentric circles.

#### Intersecting circle

Two circles which intersect each other at two distinct points are called intersecting circles.

#### Con-cyclic points

Two or more than two points which lie on the circumference of the same circle are called con-cyclic points.

A quadrilateral whose all vertices lie on the circumference of a circle is called a cyclic quadrilateral.

## Geometry: Circle Class 10 Maths Solution PDF

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## Is Class 10 Math Guide Helpful For Student ?

I have published this Notes for helping students who can't solve difficult maths problems. Student should not fully depend on this note for doing all exercises. If you totally depend on this note and simply copy a to z then it may affect your study.

Student should also try to solve some problems themselves. You can use this note as a reference. You should check all the answers carefully because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.

## How to secure good marks in Mathematics ?

As, you may know I'm also a student. Being a student is not so easy. You have to study and work hard in 8 different subjects. From my point of view most of the student are weak in mathematics. They face difficulties while solving maths problems. I was also facing the same problem when I was in grade 10.

If you also want to secure good marks in mathematics then you should practise them everyday. You should always start your practise from a simple problems. When you solve some simple problems then it will motivates you to solve some other harder problem. Slowly and gradually increase the difficulty of questions day by day.

Maths is not only about practising. You also needs to be clear about the concept of solving the problems. When you get the concept then you can easily solve maths problems which are in similar formats.

You should make the habit of making side notes. It means you should make notes of formulas, tips of solving that problems and the main concept.

When your teacher tries to make the concept clear by giving some random example then all student tries to remember the same example but you shouldn't do that. You should try to relate that concept with your daily life and create your own formula of remembering the concepts.

If you give proper time for your practise with proper method of practising then you'll definitely score a good marks in your Exam. You can also make a time table for your study and read accordingly.

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