What are the main parts of a circle?
The concept of Circles for Class 10 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Circles form the base for many geometric properties and theorems that appear in Class 10 board exams and competitive tests. Understanding circles makes geometry easier and helps students with questions in trigonometry, coordinate geometry, and daily reasoning.
What Is Circles for Class 10?
A circle is a two-dimensional closed shape consisting of all points in a plane that are at an equal distance from a fixed point, called the center. In Class 10 mathematics, circles extend beyond simple shapes to cover concepts such as radius, diameter, chord, tangent, sector, and segment. You’ll find this concept applied in areas such as symmetry, equations of circles, and angle properties within circles.
Key Formula for Circles for Class 10
Here’s the standard formula:
Area of a Circle = \( \pi r^2 \ )
Circumference of a Circle = \( 2\pi r \ )
Equation of a Circle (center at (h, k)): \( (x-h)^2 + (y-k)^2 = r^2 \ )
Parts of a Circle (With Table)
| Part Name | Definition |
|---|---|
| Center | The fixed point from which all points on the circle are equidistant. |
| Radius | A line segment from the center to any point on the circle. |
| Diameter | A chord passing through the center; longest chord (twice the radius). |
| Chord | A line segment joining two points on the circle. |
| Arc | A part of the circumference. |
| Sector | A region bounded by two radii and an arc. |
| Segment | A region bounded by a chord and its corresponding arc. |
| Tangent | A line touching the circle at exactly one point. |
| Secant | A line intersecting the circle at two points. |
Major Properties of Circles (Class 10)
- All radii of a circle are equal.
- The diameter is the longest chord and equals twice the radius.
- Equal chords are equidistant from the center.
- The tangent at any point is perpendicular to the radius at that point.
- Chords equidistant from the center are equal in length.
- Two circles are congruent if their radii are equal.
- If two tangents are drawn from an external point, their lengths are equal.
Step-by-Step Illustration: Example Problem
Let’s solve a sample problem commonly seen in Class 10 exams.
Question: From a point 25 cm away from the center of a circle (radius = 7 cm), find the length of the tangent drawn to the circle.
1. Let O be the center, OP = 25 cm, radius (OA) = 7 cm.2. OA is perpendicular to the tangent at A; consider triangle OAP (right-angled at A).
3. By Pythagoras Theorem:
\( PA^2 = OP^2 - OA^2 \)
4. Substitute values:
\( PA^2 = (25)^2 - (7)^2 = 625 - 49 = 576 \)
5. \( PA = \sqrt{576} = 24 \) cm
Final Answer: The length of the tangent is 24 cm.
Cross-Disciplinary Usage
Circles for Class 10 are not only essential in Maths but also play an important role in Physics (circular motion), Computer Science (graphics, coordinate geometry), and logical reasoning. Concepts like tangent and geometry formulas appear in JEE, NEET, and Olympiad problems. Circles represent wheels, coins, clocks, and many objects in everyday life.
Speed Trick or Vedic Shortcut
When quickly calculating circumference, use π ≈ 22/7 for easy division, especially with radii that are multiples of 7. For example, if r = 14 cm:
2 × 22/7 × 14 = 2 × 22 × 2 = 88 cm (circumference – no calculator needed!).
Common Errors and Misunderstandings
- Mixing up circle and disc: the circle is the boundary, the disc is the area inside.
- Confusing chord and diameter — diameter always passes through the center.
- Miscalculating area by forgetting to square the radius.
- Assuming tangent passes through the circle instead of touching at one point.
Interlinks For More Learning (Vedantu)
- Parts of Circle – See detailed diagrams and learn each part for exam-labeling.
- Area of Circle – Formulas, stepwise explanations, and solved practice problems.
- Circumference of a Circle – Steps to calculate perimeter with quick tricks.
- Circle Theorems – List and proofs of key theorems for higher-order problems.
Relation to Other Concepts
Understanding circles for Class 10 unlocks the door to mastering areas related to circles, coordinate geometry, and advanced theorems in mathematics. Mastering the properties of tangents and chords also makes trigonometry much easier in higher classes.
Quick Classroom Tip
To remember all major parts: “CRaD TASeS” (Center, Radius, Diameter, Tangent, Arc, Segment, Sector, Secant). Draw and label a circle each time you revise.
We explored Circles for Class 10—from definition, parts, formula, properties, solved examples, and important connections to other chapters. For in-depth theory, solved problems, and expert-prepared revision, keep practicing with Vedantu and ace your exams with confidence!
