Circle — Class 10 Maharashtra SSC Mathematics revision notes
A 5-page visual revision sheet for Circle, written for Class 10 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Circle in one look
tangents, the angles they make, and the theorems about touching rather than cutting
A line and a circle: three possibilities
- compare the perpendicular distance d from the centre to the line against the radius r
- if d > r the line misses the circle entirely and there is no common point
- if d = r the line touches at exactly one point and is called a tangent, the point being the point of contact
- if d < r the line cuts the circle at two points and is called a secant
- a chord is the part of a secant lying inside the circle, and the longest chord is the diameter
- so a tangent is the borderline case between missing and cutting, which is why d = r is its defining test
The tangent theorems
- Radius ⊥ tangent: the radius drawn to the point of contact is perpendicular to the tangent there. This is the theorem that creates a right triangle in almost every question
- Equal tangent segments: the two tangent segments drawn from an external point to a circle are equal in length, and they subtend equal angles at the centre
- Only one tangent: through a point on the circle exactly one tangent can be drawn, through an external point exactly two, and through an interior point none at all
- Tangent and chord: the angle between a tangent and a chord at the point of contact equals the inscribed angle in the alternate segment on the other side of that chord
Page 1 of 5. The full sheet, all 5 pages, opens free in the app.
What this Circle sheet covers
- Tangent
- Secant
- Point of contact
- A line and a circle: three possibilities
- Tangent theorem
- Tangent segment theorem
- The tangent theorems
- Radius ⊥ tangent
- Equal tangent segments
- Only one tangent
- Tangent and chord
- Working with the two equal tangents
- Finding a tangent length
- Touching circles
- Internally and externally touching
- Inscribed angle
- Angle in a semicircle
- Cyclic quadrilateral
- Angles in a circle, carried over from class 9
- Combining the tangent and the angle rules
- Position of a line, a point and a second circle
- Terms in this chapter
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Circle the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.