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.
Circle and Its Parts
Beyond the center, radius, and diameter, a circle has several important parts that help in understanding its geometry. A chord is a line segment joining any two points on the circle. The diameter is a special chord that passes through the center and is the longest chord possible in a circle. The arc is a part of the circle's circumference between two points. When a chord divides the circle, the arcs formed are called minor arc (smaller arc) and major arc (larger arc). A sector is the region enclosed by two radii and the arc between them, resembling a 'slice' of the circle. A segment is the region bounded by a chord and the arc it subtends. These parts are fundamental in solving problems related to circles and understanding their properties.
📊 Diagram: Fig. 10.2
🧪 Activity: Draw a circle and mark its center, radius, diameter, chord, arc, sector, and segment to visualize their relationships.
🔗 Connection: Understanding these parts is essential before exploring tangents and their properties in the following sections.
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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