ma
Circle Theorems
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
About the author
Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
Every theorem is built from these parts. An angle 'stands on' (is subtended by) an arc when its two arms reach the ends of that arc.
So if the centre angle is 80°, the edge angle is 40°. This single rule generates many others.
The semicircle case is just the centre rule with a straight line (180°) at the centre, halved to 90°.
The alternate segment theorem then links tangents to arcs: the tangent-chord angle equals the angle in the opposite segment.
Hard words & meanings
| subtended | an arc or chord subtends an angle when the angle's two arms reach its endpoints |
| inscribed angle | an angle whose vertex is on the circle and whose arms are chords |
| chord | a straight line joining two points on the circle |
| tangent | a line touching the circle at exactly one point, not crossing it |
| cyclic quadrilateral | a four-sided shape with all four corners on the circle |
| alternate segment | the part of the circle on the other side of a chord from the angle considered |
| arc | a part of the circle's edge between two points |
| central angle | an angle at the centre formed by two radii |
Model exam answers, grammar & audio
You have read the summary. The board-ready model answers, grammar notes, one-touch audio and writing practice for this chapter are part of Lipi©.
Sign in to unlockSee it, understand it, hear it read aloud, then write the exam answer with confidence, for a fraction of a tutor cost.