## Class 10 Maths Formula Circle Chapter 10

**Class-10 Maths Formula Circle**

**1. A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.2. Equal chords of a circle (or of congruent circles) subtend equal angles at the centre.3. If the angles subtended by two chords of a circle (or of congruent circles) at the centre (corresponding centres) are equal, the chords are equal.4. The perpendicular from the centre of a circle to a chord bisects the chord.5. The line is drawn through the centre of a circle to bisect a chord is perpendicular to the chord.**

**Class-10 Maths Formula Circle**

**6. There is one and only one circle passing through three non-collinear points.7. Equal chords of a circle (or of congruent circles) are equidistant from the centre (or corresponding centres).8. Chords equidistant from the centre (or corresponding centres) of a circle (or of congruent circles) are equal.9. If two arcs of a circle are congruent, then their corresponding chords are equal and conversely however**

**if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent.**

10. Congruent arcs of a circle subtend equal angles at the centre.

10. Congruent arcs of a circle subtend equal angles at the centre.

**Class-10 Maths Formula Circle**

**11. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.12. Angles in the same segment of a circle are equal.13. Angle in a semicircle is a right angle.14. If 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.15. The sum of either pair of opposite angles of a cyclic quadrilateral is 180**

**°**.16. If the sum of a pair of opposite angles of a quadrilateral is 180

**°**, the quadrilateral is cyclic.

**Class-10 Maths Formula Circle**

**Circumference of a Circle = 2***π*r**Area of Circle =***π*r^{2}**Length of the arc of the sector of angle – Length of the arc of the sector of angle***θ*/ 360° × 2*π*r**Area of the Sector of angle – Area of the sector of angle**–*θ**θ*/ 360° ×*π*r^{2}**Area of segment of a Circle – Area of the corresponding sector – Area of the Corresponding triangle**