Class 10 / Maths

Class 10 Maths Circles Worksheet

Practice tangent properties, equal tangents, and right-triangle applications in circles.

advanced40 minutesAnswer key included

Learning objective

Practise tangent definition, tangent-radius theorem, equal tangents, and right-triangle applications in circle questions.

Questions

  1. Define tangent to a circle.
  2. State the theorem connecting radius and tangent at the point of contact.
  3. How many tangents can be drawn from a point outside a circle?
  4. If two tangents PA and PB are drawn from P and PA = 12 cm, find PB.
  5. If PA = 3x + 2 and PB = 5x - 6 are tangents from P, find x.
  6. A circle has radius 6 cm. The distance from center O to external point P is 10 cm. Find tangent length PT.
  7. If OP = 13 cm and radius OT = 5 cm, find tangent PT.
  8. Explain why the radius at the point of contact is perpendicular to tangent.
  9. Can a tangent be drawn from a point inside a circle? Explain.
  10. Draw a rough figure showing two equal tangents from an external point.

Answer key

Show suggested answers
  1. A tangent is a line that touches a circle at exactly one point.
  2. The radius drawn to the point of contact is perpendicular to the tangent.
  3. Two tangents can be drawn from a point outside a circle.
  4. Tangents from the same external point are equal, so PB = 12 cm.
  5. Since PA = PB, 3x + 2 = 5x - 6. Thus 2x = 8 and x = 4.
  6. OT is perpendicular to PT. PT = sqrt(OP^2 - OT^2) = sqrt(10^2 - 6^2) = 8 cm.
  7. PT = sqrt(13^2 - 5^2) = sqrt(144) = 12 cm.
  8. A tangent touches the circle at one point, and the radius to the point of contact is perpendicular to it.
  9. No. A point inside a circle cannot have a tangent because every line through it cuts the circle at two points.
  10. The figure should show external point P, contact points A and B, and equal tangent lengths PA and PB.

How to use this worksheet

Students can solve the questions independently first, then review errors with a parent or teacher. Teachers can use it as a short class activity, homework sheet, or revision check.

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