The diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.
2 inference 1
(1) bisects the diameter (not the diameter) of the chord perpendicular to the chord and bisects the two arcs opposite to the chord.
② Chord
Moderately normal
pass by
centre of a circle
And split the two arcs opposite the chord in two.
③ bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.
3 Inference 2
Two sides of a circle
Parallel chord
The clamped arcs are equal.
A circle is centered on its center.
symcenter
about
Centrally symmetric figure
Theorem 5
In the same or equal circle, equal.
central angle
Arc is equal, chord is equal, chord is equal.
Chord center distance
(to) equal to ...
6 inference
If two central angles, two arcs, two chords or
Two strings
If one set of quantities in the distance from the chord to the center is equal, then the other set of quantities corresponding to it is also equal.
Theorem 7
The arc is right.
circumferential angle
Equal to half the central angle it subtends.
8 Inference 1
The same arc or
equal arcs
The circumferential angle is equal; In the same circle or in the same circle, the arcs of equal circumferential angles are also equal.
9 Inference 2
The circumference angle (or diameter) of a semicircle is a right angle; A chord with a circumferential angle of 90 is a diameter.
10 inference 3
If the median line of one side of a triangle is equal to half of this side, then this triangle is
right triangle
Theorem 1 1
inscribed circle
quadrilateral
about
opposite angles
Complementary, any one
exterior angle
That makes no difference.
Inner/inner diagonal
12
①
straight line
L and o intersect
dr
13
tangent
Decision theorem of
The straight line passing through the outer end of the radius and perpendicular to the radius is the tangent of the circle.
Property Theorem of Tangent of 14
The tangent of the circle is perpendicular to it.
point of tangency
Radius of
15 inference 1
A straight line passing through the center of the circle and perpendicular to the tangent must pass through the tangent point.
16 inference 2
A straight line that passes through the tangent and is perpendicular to the tangent must pass through the center of the circle.
17 tangent length theorem
Two tangents drawing a circle from a point outside the circle have the same length, and the straight line connecting the center of the circle and the point bisects the two tangents.
street corner
18 round
restricted
Two groups of quadrangles
Opposite width
Equal sum
19 chord angle theorem
The chord tangent angle is equal to the circumferential angle of the arc pair it clamps.
20 inference
If the arc enclosed by two chord angles is equal, then the two chord angles are also equal.
2 1 intersection chord theorem
Two lines in a circle
Intersecting chord
exist
Intersection
one divides into two—everything has its good and bad sides
line segment
Long product is equal.
22 Inference
If the chord intersects the diameter vertically, half of the chord is divided into two sections formed by the diameter.
proportion
Zhongfu
23 cutting line theorem
The sum of the tangent lines of the circle is drawn from a point outside the circle.
secant
The tangent length is the median in the length ratio of two lines from this point to the intersection of secant and circle.
24 inference
Draw two secants of a circle from a point outside the circle, and the product of the lengths of the two lines from that point to the intersection of each secant and the circle is equal.
If two circles are tangent, then the tangent point must be at.
Lian Xin line
Last/better/previous/last name
26
① The two circles are separated from each other.
d>R+r
(2) circumscribe two circles.
d=R+r
③ Two circles intersect.
R-rr)
⑤ two circles contain d < r-r (r > r).
Theorem 27
Divide the two circles vertically with a straight line connecting them.
Gong * * * string
Theorem 28
Divide a circle into n(n≥3):
(1) connect each one in turn.
equinox
income
The polygon of is inscribed in this circle.
Regular n polygon
(2) The tangent of a circle passing through each point is defined as the intersection of adjacent tangents.
pinnacle
The polygon of is the circumscribed regular n polygon of this circle.
Theorem 29
Any regular polygon has one.
circumcircle
And an inscribed circle, these two circles are
concentric circles
30
Internal common tangent
Length =
d-(R-r)
External common tangent length =
d-(R+r)
3 1
Area formula
: ①S positive δ =-
-×(
Length of side
)2.-②S
parallelogram
= bottom × height. ③S
diamond
= bottom × height =-
-×(
Maomaojiao
Products)
-④S circle =πR2. ⑤C
circumference
=2πR.⑥
Radian wavelength
L=-
-.-⑦S
department
=-
-=-
-LR。 ⑧S
column
Side =
the seamy side
Circumference × height. -⑨S
circular cone
Edge =-
-× Bottom circumference ×
bus
=πrR and-2π r.
32 Arc length formula: Arc length =θ*r
θ is the angle.
R is the radius.
l=nπr÷ 180
In a circle with radius r, because the arc length corresponding to the central angle of 360 is equal to the circumference of the circle c = 2π r, the arc length corresponding to the central angle n is L = nπ r ÷ 180.