Point of contact
- CBSE · NCERT Class 10, Ch 10 Circles
The point of contact is the single point where a tangent touches a circle.
A tangent meets its circle at one point only. That point is the point of contact. The radius drawn to it is at right angles to the tangent. So the centre, the point of contact and any point on the tangent form a right triangle. Pythagoras then gives the missing side.
A small example
A circle has centre O and radius 7 cm. A tangent from a point P touches it at T, and OP = 25 cm. The angle at T is 90°. So PT² = 25² − 7² = 625 − 49 = 576, and PT = 24 cm.
Where marks go
Question 37(ii) of CBSE's 2026-27 Maths Standard sample paper asks for the length of a tangent. The radius is 9 m and the point is 18 m from the centre. In the 2026-27 Maths Standard marking scheme, the equation OP² = OA² + AP² earns half a mark. The length, 9√3 m, earns the other half.
The equation only makes sense because of the right angle at the point of contact. Writing it down is itself a marked step. See how step marking works.
Sources
Facts last checked against these sources on 30 September 2026.
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