NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Area of Circles

Area of Circles
S. noPoints
1A circle is a collection of all the points in a plane, which are equidistant from a fixed point in the plane
2Equal chords of a circle (or of congruent circles) subtend equal angles at the center.
3If the angles subtended by two chords of a circle (or of congruent circles) at the center (corresponding center) are equal, the chords are equal.
4The perpendicular from the center of a circle to a chord bisects the chord.
5The line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
6There is one and only one circle passing through three non-collinear points
7Equal chords of a circle (or of congruent circles) are equidistant from the center (or corresponding centers) .
8Chords equidistant from the center (or corresponding centers) of a circle (or of congruent circles) are equal
9If two arcs of a circle are congruent, then their corresponding chords are equal and conversely, if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent.
10Congruent arcs of a circle subtend equal angles at the center.
11The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle
12Angles in the same segment of a circle are equal
13Angle in a semicircle is a right angle.
14If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle.
15The sum of either pair of opposite angles of a cyclic quadrilateral is .
16If the sum of a pair of opposite angles of a quadrilateral is 180°, then the quadrilateral is cyclic.
Area of Circles
S. noTermsDescription
1Circumference of a circle
2Area of circle
3Length of the arc of the sector of angleLength of the arc of the sector of angle

4Area of the sector of angleArea of the sector of angle

5Area of segment of a circleArea of the corresponding sector — Area of the corresponding triangle