Circle

Circle - basic concepts

$k(O,r)$ - circle k with center point O and radius r
$AB=d=2r$ - diameter
$MN$ - chord
$l$ - length


$$l=2πr$$ $$l=πd$$

Circle and point

$OM < r$ M - in the circle
$ON = r$ N - on the circle
$OP > r$ P - out of the circle

Circle and line

$OA < r$ a - secant
$OB = r$ b - tangent
$OC > r$ c - out of the circle

Circle and angle

$∢AOB$ - central
$OM = r$

$$m∢AOB=m{AB}↖{\^}$$

$∢AMB$ - circumscribed
$$m∢AMB={m{AB}↖{\^}}/2$$

$OM < r$
$∢AMC$ - in the circle

$$m∢AMC={m{AC}↖{\^}+m{BD}↖{\^}}/2$$

$$α=β=γ={m{AB}↖{\^}}/2$$

$$AB = d$$
$$m{AB}↖{\^} = 180°$$
$$α=β=γ=90°$$

Disk area

$$S=πr^2$$
$$S={πd^2}/4$$
$$S={ld}/4$$