Tangent to a circle

A line and a circle can meet in three ways. They may not meet at all. The line may cut the circle at two points, which makes it a secant. Or it may touch the circle at just one point. That line is a tangent.

The key fact is a theorem in the chapter. A tangent is at right angles to the radius drawn to the point where it touches. Every tangent question uses this right angle.

A small example

From a point P, two tangents touch a circle with centre O at A and B. The angle APB is 70°. In the shape OAPB, the angles at A and B are 90° each. The four angles add to 360°. So angle AOB = 360° − 90° − 90° − 70° = 110°.

Where marks go

Question 37 of CBSE's 2026-27 Maths Standard sample paper is a case study about a round garden. Part (i), worth 1 mark, asks for angle OAP. The 2026-27 Maths Standard marking scheme gives 90° with its reason beside it. The radius is at right angles to the tangent. The next two parts build on that right angle.

Writing the reason next to each step shows the examiner which fact you used. See how step marking works.

About the author

Mohit Sardana

Chief Architect

An engineer (B.Tech, Computer Science) with over 20 years of preparing students for entrance exams, including as Dean at FIITJEE and Vice-President at Aakash. He is the chief architect of the TRUpreBoards evaluation engine.

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