CBSE Class 7 Mathematics Practical Geometry Notes

CBSE Class 7 Practical Geometry Concepts. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Practical Geometry

10.1 Circle

A circle is a set of points which are all a certain distance from a fixed point known as the centre.

Radius of the circle:  A line joining the centre of a circle to any of the points on the circle is known as its radius.

Circumference of a circle: The circumference of a circle is the length of the circle.  The circumference of a circle = 2 × π × radius = 2 π r units.

Chord: A line which touches the circle at two distinct points is called a chord. The line AB in the second diagram represents a chord. It divides the circle into a major segment and a minor segment.

Length of the Perpendicular: The length of the perpendicular from a point P to a line (l) is the distance of the line from the point. i.e. PF

10.2 Tangents

A tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle- it just touches it).

Length of Tangents:  The length of the segment of the tangent from the external point P and the point of contact with the circle is called the length of the tangent from the point P to the circle.

10.3 Theorems

Theorem – 1: Angles Subtended on the Same Arc: Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points. i.e. Angles in the same segment of a circle are equal. 

Theorem – 2: Angles in a Semi-Circle: Angle in a semi circle is right angle.

Theorem – 3: Equal chords of a circle subtend equal angles at the centre

Theorem – 4 (Converse theorem – 3): If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Theorem – 5: The perpendicular from the centre of a circle to a chord bisects the chord.

Theorem – 6 (converse of theorem - 5: The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Theorem – 7: There is one and only one circle passing through three given non-collinear points.

Theorem – 8: Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

Theorem – 9: Chords equidistant from the centre of a circle are equal in length

Theorem – 10: A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent. Or The tangent at any point of a circle is perpendicular to the radius through the point of contact

Theorem – 11: If two tangents are drawn on a circle and they cross, the lengths of the two tangents (from the point where they touch the circle to the point where they cross) will be the same. Or The lengths of tangents draw from an external point to a circle are equal. PA = PB

Theorem – 12 Angle at the Centre (angle measure theorem of a circle): The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b.

Theorem – 13 Alternate Segment Theorem: This diagram shows the alternate segment theorem. In short, <1 = <2 and <3 = <4

10.4 Area of Sector and Arc Length

If the radius of the circle is r, Area of sector = πr² × A/360  sq. units Arc length = 2πr × A/360 units

In other words, area of sector = area of circle × A/360 arc length = circumference of circle × A/360