NCERT Mathematics, Class 10, textbook pages 144–153

How to help your child with Class 10 Maths Chapter 10, Circles, at home

Tangents to a circle, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

PAPBPA = PB; radius ⟂ tangent

NCERT Class 10 Maths Chapter 10 Circles: what it teaches

Your teen learns that a tangent touches a circle at one point, is perpendicular to the radius there, and that tangents from an external point are equal in length.

Why it matters later. Tangent properties are used in coordinate geometry and calculus (tangent lines).

See it: this chapter in pictures

radius ⟂ tangentOP = 13, r = 5tangent = √(169 − 25) = 12
Right angle at the point of contact.
from an external pointexactly 2 tangentsequal in length
The equal tangents theorem.
inside the circle: 0 tangentson the circle: 1outside: 2
Position decides the count.

You need

  • compass, ruler, set square
  • a round lid

Tonight’s 45 minutes

  1. Draw a circle and a tangent at a point. Measure the angle with the radius (90°).
  2. From an external point, draw two tangents and measure their lengths.
  3. Solve: tangent from a point 13 cm from the centre, radius 5 cm (12 cm).
  4. Prove tangents from an external point are equal.

Words to use

  • tangent
  • secant
  • point of contact
  • radius
  • external point

Watch for

  • Drawing a tangent that cuts the circle. A tangent touches at exactly one point.
  • Missing the right angle in diagrams. Always mark radius ⟂ tangent.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouRadius 5, distance 13. Tangent?

Your child√(169 − 25) = 12.

A game for this week: Tangent check

  1. Draw circles and external points.
  2. Draw tangents with a ruler.
  3. Measure lengths.
  4. Check they are equal.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Wheels touching roads.
  • Belt and pulley systems.
  • Circular tracks.
  • Gear design.

Quick check

Ask these at the end of the week. Tap to see the answer.

Angle between tangent and radius?

90°.

Tangent length from a point 13 cm away, radius 5?

12 cm.

How many tangents from an external point?

2.

Ready for the next chapter when your child…

  • States tangent properties.
  • Uses right angle at contact.
  • Proves equal tangents theorem.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

What is a tangent?

A line touching a circle at exactly one point.

Why is the tangent perpendicular to the radius?

The radius is the shortest distance from the centre to the tangent.

Are constructions included?

Tangent constructions may be deleted in the current syllabus; check.