Circle — Class 9 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Circle, written for Class 9 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
chords and arcs, the perpendicular from the centre, and the circle through three points
The parts of a circle
- a circle is the set of all points at a fixed distance, the radius, from a fixed point, the centre
- a chord joins any two points of the circle, and the longest chord is the diameter, which passes through the centre
- an arc is a piece of the circle itself, the minor arc being the shorter of the two a chord cuts off and the major arc the longer
- a segment is the region between a chord and its arc, while a sector is the region between two radii and their arc
- so a segment is cut off by a chord and a sector by two radii, which is the distinction most often confused
- concentric circles share a centre but have different radii
The chord theorems
- the perpendicular drawn from the centre to a chord bisects the chord, and this is the workhorse of the chapter
- the converse is also true: the line from the centre to the midpoint of a chord is perpendicular to it
- equal chords are equidistant from the centre, and chords equidistant from the centre are equal
- so the longer the chord, the closer it lies to the centre, and the diameter passes through the centre itself
- equal chords subtend equal angles at the centre, and the converse holds
- equal chords also cut off equal arcs, and equal arcs subtend equal angles at the centre
Why the perpendicular bisects the chord
- let AB be a chord of a circle with centre O, and let OM be perpendicular to AB
- join OA and OB, which are both radii
- compare △OMA and △OMB
- OA = OB, both being radii of the same circle
- ∠OMA = ∠OMB = 90°, since OM is perpendicular to AB, and OM = OM is common
- so by the RHS test the two triangles are congruent, and therefore AM = MB by corresponding parts
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Circle sheet covers
- Chord
- Arc
- Segment
- Sector
- The parts of a circle
- Perpendicular from the centre to a chord
- Equal chords
- The chord theorems
- Why the perpendicular bisects the chord
- The lengths this chapter computes
- half chord, radius and distance from centre
- so the chord length from r and d
- and the distance from centre from r and c
- circumference of the whole circle
- area of the whole circle
- Chord length from the radius
- Circle through three points
- Circumcircle
- Concyclic points
- The circle through given points
- Arcs and the angles they subtend
- Segment against sector, and minor against major
- 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.