Circles
Madhya Pradesh Board · Class 10 · Mathematics
Summary of Circles for Madhya Pradesh Board Class 10 Mathematics. Key concepts, important points, and chapter overview.
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A circle and a line can meet in three different ways: the line may not meet the circle at all, it may cut the circle at two points, or it may touch the circle at exactly one point. A line that touches a circle at one point is called a tangent. The chapter also studies the key properties of tangents,
Key Concepts
A line may have no common
A line may have no common point with a circle, two common points, or exactly one common point. These three positions are called non-intersecting line,
The common point of a tangent
The common point of a tangent and the circle is called the point of contact.
A tangent is a secant when
A tangent is a secant when the two end points of its corresponding chord coincide.
The tangent at any point
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
There is no tangent through
There is no tangent through a point inside the circle, exactly one tangent through a point on the circle, and exactly two tangents through a point out
Learning Objectives
- Identify the three possible positions of a line with respect to a circle
- Define secant, tangent, and point of contact
- Understand that a tangent is a special case of a secant
- Use Theorem 10.1 to prove that a tangent is perpendicular to the radius at the point of contact
- Recognise that only one tangent passes through a point on the circle, none through a point inside, and exactly two through a point outside
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