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C. I. R. C. L. E. S. Basic Class VII Terms. Extra Terms. New Theory. Known Theories. Click on the desired option. Exit. Back. Basic Terms.

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Presentation Transcript
slide1

C

I

R

C

L

E

S

slide2

Basic

Class VII

Terms

Extra

Terms

New

Theory

Known

Theories

Click on the desired option

Exit

slide3

Back

Basic Terms

A line segment which passes through the centre of a circle and has its end points on the boundary on the circle is called a diameter of the circle.

Any straight line drawn from any two end points on the circle

A line segment with one end point at the centre of a circle and the other on the boundary of the circle, is called a radius of a circle

O

slide4

The diameter of a circle divides the circle into two equal parts. Each part is called a semicircle.

O

slide5

Y

X

A line segment with its end points lying on the boundary of the circle is known as a chord of the circle.

A

The part of a circle included between two points on the circle is called an arc of the circle.

B

If the length of the arc Is less than the length of the arc of the semicircle then the arc is called a minor arc of the circle.

If the length of the arc Is more than the length of the arc of the semicircle then the arc is called a major arc of the circle.

slide6

Y

X

The chord AB of this circle, divides the circle into two parts. Each part is known as a segment of the circle.

A

AXB is a major segment of the circle.

B

AYB is a minor segment of the circle.

slide7

A

B

C

D

If all four vertices of a quadrilateral lie on a circle then it is called a cyclic quadrilateral.

slide9

Back

X

Y

Extra Terms

A secant is a line that intersects a circle in two distinct points.

XY is a secant

slide10

X

Y

A line that touches a circle in exactly one point is called a tangent to the circle.

R

slide11

X

B

A

o

Z

Degree measure of arc AXB

If each endpoint of an arc of a circle is joined to the centre of the circle, the measure of the angle formed at the centre is called the degree measure of the arc.

O

The region enclosed by the arc AXB and the radii OA and OB is called the sector of the circle.

Two arcs which have the same length are known as congruent arcs.

slide13

Back

Known Theories

A

B

O

C

All angles in a semicircle are 90 degree angles.

slide14

C

D

B

A

All angles in the same segment are equal.

In this case, angle ACB and ADB are equal.

Even angle DBC and DAC are equal.

1. All angles in a major segment are acute angles.

And all angles in a minor segment are obtuse.

slide15

C

A

B

D

Angle ACB is in the major segment, while angle ADB is in the minor segment. Since the quadrilateral formed has all four vertices on the circle, it forms a cyclic quadrilateral.

So… angle D + angle B = 180 degrees.

slide17

New Theory

X

O

A

B

C

The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

In this diagram, angle AOB is twice that of angle ACB.

slide19

Math Project

Circles

Class VII

Rhea Karia

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