Length of a tangent
- CBSE · NCERT Class 10, Ch 10 Circles
The length of a tangent is the distance from an outside point to the point where the tangent from it touches the circle.
From a point outside a circle, you can draw exactly two tangents. A theorem in the chapter says these two lengths are always equal. The distance runs from the outside point to the point of contact. This one fact solves many questions about shapes drawn around a circle.
A small example
A four-sided shape ABCD is drawn around a circle, so each side is a tangent. Each corner sends two equal tangents to the circle. Adding them up gives AB + CD = AD + BC. If AB = 6 cm, BC = 7 cm and CD = 8 cm, then AD = 6 + 8 − 7 = 7 cm.
Where marks go
Question 29 of CBSE's 2026-27 Maths Standard sample paper asks for a proof. A parallelogram drawn around a circle must be a rhombus. The 2026-27 Maths Standard marking scheme gives 1 mark for writing the four pairs of equal tangents with the reason. It gives 1 mark for adding them, and 1 mark for the conclusion.
In the Maths Basic sample marking scheme, Question 24 gives half a mark for each pair of equal tangents. The length asked earns 1 mark. Stating the equal pairs is a marked step in both. See how step marking works.
Sources
Facts last checked against these sources on 30 September 2026.
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