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Math Ch 11 Circles - Coggle Diagram
Math Ch 11 Circles
11.2 Properties of Chords of a Circle
Theorem 1
★★Perpendicular from centre to chord
Bisects chord
Result
Reason
Sometimes may test, 50/50 (2 stars)
Can be proved by RHS (not needed in tests)
Theorem 2
Line joining centre to mid-pt. of chord
⟂ chord
Theorem 3(very unimportant)
⟂ bisector of chord passes through centre
Likely MC
Theorem 4
★★Equal chords,
Equidistant from centre
Theorem 6
★★★∠ at centre twice ∠ at circumference ☉
Theorem 5
Chords equidistant from centre are equal
Theorem 7
★★★∠ in semi circle
90 degree
Theorem 8 (Converse of Theorem 7)
★★★ ∠ Converse of in semi circle
Theorem 9
★★ ∠s in the same segment
Theorem 10
Special circles
Equal circles
Concentric circles
Same center
Circumscribed circle / circumcircle
Passes through each vertex of a polygon
Inscribed circle
Touches each side of a polygon at 1 point
Basic
Circumference
Between 2 points
Radius
Diameter
/2
Arcs and Sectors
Shorter: minor arc
Bounded by 2 radii
" sector
Longer: major arc
Bounded by chord
" segment
Same: semi-circle
11.2 Angle Properties of a Circle
1
Angle at centre
Angle at circumference
2
Reflex ∠AOB
Angle at centre
∠AQB
Angle at the circumference