Circles Class 10 Maths — Revision Notes
This chapter explores properties of circles including tangents, chords, and angles subtended by arcs. Students learn about circle theorems and tangent-chor
TL;DR: This chapter explores properties of circles including tangents, chords, and angles subtended by arcs. Students learn about circle theorems and tangent…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
This chapter explores properties of circles including tangents, chords, and angles subtended by arcs. Students learn about circle theorems and tangent-chor
Circle Basics
- Circle is locus of points equidistant from center
- Radius is distance from center to circumference
- Diameter is longest chord passing through center, d = 2r
- Circumference = 2πr, Area = πr^2
Tangent and Chord
- Tangent is line touching circle at exactly one point
- Tangent is perpendicular to radius at point of contact
- Chord is line segment joining two points on circle
- Perpendicular from center bisects chord
Angles and Arcs
- Angle subtended at center is twice angle subtended at circumference
- Angles in same segment are equal
- Angle in semicircle is right angle (90°)
- Opposite angles in cyclic quadrilateral sum to 180°
Tangent-Secant Properties
- From external point, tangent and secant can be drawn to circle
- Two tangents from external point are equal in length
- Angle between tangent and chord equals angle in alternate segment
- If tangent and secant drawn from point: (tangent)^2 = (external part of secant) x (whole secant)
Key Terms
- Tangent: Line touching circle at exactly one point and perpendicular to radius
- Chord: Line segment joining two points on circle
- Cyclic Quadrilateral: Quadrilateral whose all vertices lie on a circle
Frequently Asked Questions
What is angle in a semicircle?
Angle subtended by diameter at any point on circle is 90 degrees (right angle).
Why are two tangents from external point equal?
Both tangents from external point to center form right triangles. Since radius is same and hypotenuse (from external point to center) is same, tangent lengths are equal.
More Class 10 Maths Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
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