Circles | Class 10 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 3 min read
Circles – this guide gives you a concise, exam-ready overview of Circles from Class 10 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
Introduction
A circle is one of the most fundamental shapes studied in geometry. It is defined as the set of all points in a plane that are at a fixed distance from a fixed point. This fixed point is called the center of the circle, and the fixed distance is called the radius. The circle is a closed curve and is perfectly symmetrical about its center. The radius is a line segment joining the center to any point on the circle. The diameter is a special chord that passes through the center and is twice the length of the radius. Circles are widely found in nature and human-made objects, such as wheels, coins, and clocks, making their study important in both theoretical and practical contexts.
📊 Diagram: (i); (ii); (iii)
🧪 Activity: Observe various circular objects around you and identify the center, radius, and diameter in each.
🔗 Connection: This introduction sets the foundation for understanding the parts of a circle and their properties, which are discussed in the next section.
Frequently asked questions
1. How many tangents can a circle have?
A circle can have infinitely many tangents. At every point on the circle, there is exactly one tangent line. Since a circle has infinitely many points, it has infinitely many tangents.
2. Fill in the blanks : (i) A tangent to a circle intersects it in point (s). (ii) A line intersecting a circle in two points is called a . (iii) A circle can have parallel tangents at the most. (iv) The common point of a tangent to a circle and the circle is called .
(i) A tangent to a circle intersects it in point (s): one point. (ii) A line intersecting a circle in two points is called a secant. (iii) A circle can have parallel tangents at the most: two. (iv) The common point of a tangent to a circle and the circle is called point of contact.
3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is : (A) 12 cm (B) 13 cm (C) 8.5 cm (D) 119 cm.
Given: Radius OP = 5 cm, OQ = 12 cm, PQ is tangent at P. Since PQ is tangent at P, OP ⊥ PQ. In right triangle OPQ, by Pythagoras theorem: PQ² + OP² = OQ² => PQ² = OQ² - OP² = 12² - 5² = 144 - 25 = 119 => PQ = √119 ≈ 10.91 cm None of the options exactly match 10.91 cm, but closest is (C) 8.5 cm is less, (B) 13 cm is close. Rechecking the problem setup: Possibly OQ is the distance from centre to Q on the line through O and tangent at P. Actually, since PQ is tangent at P, and Q lies on the line th
4. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
To solve this, first draw a circle. Then draw a given line. Draw one line parallel to the given line such that it touches the circle at exactly one point (tangent). Draw another line parallel to the given line such that it intersects the circle at two points (secant). This satisfies the condition.
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