Tangents to a circle: the tangent is perpendicular to the radius at the point of contact, and the two tangents from an external point are equal. Our own step-by-step solutions to Exercises 10.1 and 10.2, one page per exercise, set out for step marks.
Each exercise has its own page with every question solved step by step. Pick the one you are on.
What it tests. A tangent meets the circle at exactly one point (the point of contact); a secant meets it at two. Through each point of the circle there is exactly one tangent, so a circle has infinitely many tangents, and at most two of them are parallel to a given line.
What it tests. Theorem 1: the tangent at any point is perpendicular to the radius through that point. Theorem 2: the lengths of the two tangents from an external point are equal. Most questions combine these with Pythagoras or with angle sums in the quadrilateral OAPB.
Circles has 38 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Circles · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.