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Circle - Basic Introduction to circle for class 10th maths.
This document provides an overview of circles, defining key concepts such as chord, diameter, radius, circumference, arc, secant, sector, and tangent. It explains the properties and relationships of these elements in relation to a circle, highlighting differences between intersecting and non-intersecting lines. Additionally, it summarizes the essential characteristics of circles and their components.
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Circle - Basic Introduction to circle for class 10th maths.
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- 2. Objectives After completingthis module, you will be able to, Define a circle Define circle basics (chord, segment , sector, acr, secant, etc) Define intersecting line, non-intersecting line and tangent.
- 3. Circle (Basics) Acircle is a shape with all points at the same distance from its A B E O = = = C D Radius It’s the distance from the center of a circle to any point on the circle. Diameter Centre of circle Circumference centre. It’s the distance across a circle through the center. All points on the circle are at same distance from the centre point. It’s the distance around the circle.
- 4. Chord A chordis a straight line segment with its end points on the circumference of a circle A Chord Chord B E O Diameter, the biggest chord Interior of the circle Exterior of the circle
- 5. Arc An arcis a part of a circumference of a circle. O M N Chord Major Arc Minor Arc Minor Segment Major Segment 1 2
- 6. Secant If theline segment that forms a chord of a circle is extended on both the sides, the straight line with two points on the circle is known as a secant. O A B Chor d Secant
- 7. Sector Sector ofa circle is a portion of a circle enclosed by two radii and an arc. O Major Sector Radius Radius A B Minor Sector
- 8. Circle and aLine in a Plane O Secant Line AB and the circle have two common points M and N Tangent There is only one point P which is common to the line AB and the circle A B O M N O P Non-intersecting Line Line AB and the circle have no common points
- 9. Summary Let usrevise what we have learnt in this session. A circle is a collection of all points in a plane which are at a constant distance from a fixed point. Radius is the distance from the center of a circle to any point on the circle. Diameter is the distance across a circle through the center. Circumference is the distance around the circle. A chord is a straight line segment with its end points on the circumference of a circle
- 10. Summary Anarc is a part of a circumference of a circle. If the line segment that forms a chord of a circle is extended on both the sides, the straight line with two points on the circle is known as a secant. Sector of a circle is a portion of a circle enclosed by two radii and an arc. Intersecting line have two common points & Non-intersecting line have no common points with the circle. Tangent have only one common point with the circle.
Editor's Notes
- #2 Today we are going to revise some basic terms related to circles.
- #3 Objectives: After completing this module, you will be able to, Describe a tangent to a circle Define circle basics(chord, segment, sector, arc, secant, etc) Define intersecting line, non-intersecting line and tangent.
- #4 Let us revise the concept of a circle. This is a point O in a plane. A circle is a collection of all points in a plane which are at a constant distance from the point O. If A, B, C, D and E are the points of the circle, then, length OA is equal to length OB is equal to length OC is equal to length OD is equal to length OE. Point O is called centre of the circle. OA, OB, OC, OD and OE are the radii of the circle. BE is the diameter of the circle and this is arc is the circumference of the circle.
- #5 Audio Script: A chord is a straight line segment with its end points on the circumference of a circle. If we join any two points on the circle, it is called as chord of a circle. Here, AB, AE and BE are the Chords of the circle. Diameter is the biggest chord of a circle. The portion inside the circle is known as interior of the circle while the portion outside the circle is known as exterior of the circle.
- #6 Audio Script: An arc is a part of a circumference of a circle. If segment MN is a chord, then, Arc MN-1 is known as the minor arc and arc MN-2 is known as the major arc. The interior region of a circle between a chord and an arc of a circle is known as a segment.
- #7 Audio Script: If the line segment that forms a chord of a circle is extended on both the sides, the straight line with two points on the circle is known as a secant.
- #8 Audio Script: Sector of a circle is a portion of a circle enclosed by two radii and an arc. The area enclosed by radii and major arc is known as Major Sector and the area enclosed by radii and minor arc is known as Minor Sector.
- #9 Audio Script: Let us now observe the different situations that can arise when a circle and a line are given in a plane. Consider a circle with centre O and a line AB. There can be three possibilities. The line AB and the circle have no common point. Then, the line AB is called a non-intersecting line with respect to the circle. There are two common points M and N that the line AB and the circle have. That is, the line AB intersects the circle in two points, M and N. Then, the line AB is called as a secant of the circle. There is only one point P which is common to the line AB and the circle. Then, the line AB is called a tangent to the circle.
- #10 Audio Script Let us revise what we have learnt in this session. A circle is a collection of all points in a plane which are at a constant distance from a fixed point. If a circle and a line are given in a plane, then the line can be a non-intersecting line with respect to the circle or the line can be a secant of the circle. If there is only one point which is common to the line and the circle, the line is called a tangent to the circle. The tangent at any point of a circle is perpendicular to the radius through the point of contact.
- #11 Audio Script Let us revise what we have learnt in this session. A circle is a collection of all points in a plane which are at a constant distance from a fixed point. If a circle and a line are given in a plane, then the line can be a non-intersecting line with respect to the circle or the line can be a secant of the circle. If there is only one point which is common to the line and the circle, the line is called a tangent to the circle. The tangent at any point of a circle is perpendicular to the radius through the point of contact.