Class 10 Maths — Chapter 10: CIRCLES

What you'll learn

• ▸Tangent, Secant, and Non-intersecting Lines
• ▸Tangent as a Special Case of a Secant
• ▸Theorem 10.1: Tangent-Radius Perpendicularity
• ▸Number of Tangents from a Point
• ▸Theorem 10.2: Lengths of Tangents from an External Point
• ▸Problem Solving with Tangent Properties

Chapter Summary

--- PAGE 1 --- 1062CH10 CIRCLES 10 10.1 Introduction You have studied in Class IX that a circle is a collection of all points in a plane which are at a constant distance (radius) from a fixed point (centre). You have also studied various terms related to a circle like chord, segment, sector, arc etc. Let us now examine the different situations that can arise when a circle and a line are given in a plane. So, let us consider a circle and a line PQ. There can be three possibilities given in Fig. 10.1 below: P P P A A B Q Q Q (i) (ii) (iii) Fig. 10.1 In Fig. 10.1 (i), the line PQ and the circle have no common point. In this case, PQ is called a **non-intersecting** line with respect to the circle. In Fig. 10.1 (i…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Illustrate tangents in everyday objects. Get Solution →
2. Explain why Pi is so important for circles. Get Solution →
3. Discover where circles appear in nature. Get Solution →
4. What is a line called if it intersects a circle at two distinct points? Get Solution →
5. According to the text, how many points does a tangent have in common with the circle it touches? Get Solution →
6. What is the common point between a tangent and a circle called? Get Solution →
7. How many tangents can be drawn to a circle from a point lying inside it? Get Solution →
8. A line that has no common point with a circle is called a... Get Solution →

Did you know?

• 💡 The number Pi, vital for circles, has an infinite non-repeating decimal expansion.
• 💡 Rainbows are full circles, but we only see an arc due to our viewpoint.
• 💡 Ancient Egyptians used circles to accurately survey land after Nile floods.
• 💡 When a bicycle wheel rolls, the ground forms a tangent at the contact point.
• 💡 The word "tangent" means "to touch" in Latin, referring to its single contact point.

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