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This is a mind map about circles. The main contents include: cultivating the ability to analyze and solve problems, determining the conditions of a circle, the relationship between the circumferential angle and the central angle, circles, the perpendicular diameter theorem, and the symmetry of circles.
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- Reproductive system
This template shows the structure and function of the reproductive system in the form of a mind map. It introduces the various components of the internal and external genitals, and sorts out the knowledge clearly to help you become familiar with the key points of knowledge.
- Interpretation and summary of relationship field e-book
This is a mind map about the interpretation and summary of the relationship field e-book, Main content: Overview of the essence interpretation and overview of the relationship field e-book. "Relationship field" refers to the complex interpersonal network in which an individual influences others through specific behaviors and attitudes.
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This is a mind map about accounting books and accounting records. The main contents include: the focus of this chapter, reflecting the business results process of the enterprise, the loan and credit accounting method, and the original book of the person.
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- Outline
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Relationship between circumferential angle and central angle
Can identify circumferential angles
The vertices of the three angles are on the circle, and the parts on both sides of them inside the circle are the chords of the circle.
Circle angle theorem and corollary
Circle Angle Theorem
The measure of a circumferential angle is equal to half the measure of the central angle on the arc it subtends.
The measure of a circumferential angle is equal to half the measure of the arc it subtends
The circumferential angles subtended by congruent arcs or congruent arcs are equal
The circumferential angle subtended by the diameter is a right angle, and the chord subtended by the 90° circumferential angle is the diameter.
Use circle angles to solve related calculation and reasoning problems
Solve its related computational and proof problems
Pay attention to the use of auxiliary lines
Develop analytical and problem-solving skills
Determine the conditions for a circle
Three points that are not on the same straight line determine a circle
Understand the characteristics of the circumcircle of a triangle, the circumcenter of a triangle, etc.
The circle passing through each vertex of a triangle is called the circumcircle of the triangle
The center of the circumcircle is the intersection point of the perpendicular bisectors of the three sides of the triangle, which is called the circumcenter of the triangle.
This triangle is called the inscribed triangle of the circle
Complementary diagonals of a quadrilateral inscribed in a circle
Any exterior angle of a quadrilateral inscribed in a circle is equal to its opposite interior angle
Five Hearts of Triangle
outer center
The intersection point of the perpendicular bisectors of the three sides of a triangle, which is the center of the circumcircle of the triangle. The distances from the circumcenter to the three vertices of a triangle are equal
heart
The intersection point of the three interior angle bisectors of a triangle is the center of the inscribed circle of the triangle. The distance from the center to the three sides of the triangle is equal
center of gravity
The intersection of the three midlines of a triangle is twice as far from the vertex as the midpoint. The center of gravity also divides the triangle into six smaller triangles of equal area.
Be sincere
The intersection point of the three heights of a triangle. In an acute triangle, the perpendicular is located inside the triangle; in a right-angled triangle, the perpendicular is located at the vertex of the right angle; in an obtuse triangle, the perpendicular is located outside the triangle
Pay attention
The intersection of one interior angle bisector of a triangle and the other two exterior angle bisectors. Each triangle has three circumcenters, all of which are outside the triangle. The distances from the circumcenter to the three sides of the triangle are equal
Can draw
circle symmetry
Identical circles and equal circles
In congruent circles or congruent circles, equal central angles subtend arcs that are equal and subtend chords that are equal.
what is arc
A semicircle is an arc, but an arc is not necessarily a semicircle
An arc of one degree? significance
Divide the entire circle into 360 parts, and each such arc is called an arc of 1°
The measure of the central angle of a circle is equal to the measure of the arc it subtends
In the same circle or equal circles, two arcs that can overlap are called equal arcs.
what is string
The radius is the chord, but the chord is not necessarily the radius
The line segment connecting any two points on a circle is called a chord
central angle theorem
In congruent circles or equal circles, if one set of quantities in two central angles, two arcs, and two chords are equal, then the remaining sets of quantities corresponding to them are equal respectively.
The two endpoints of any diameter of a circle divide the circle into two equal arcs, each arc is called a semicircle
A circle is a centrally symmetrical figure, and the center of symmetry is the center of the circle
A circle is an axially symmetrical figure, and its axis of symmetry is any straight line passing through the center of the circle.
Perpendicular diameter theorem
Understand the vertical diameter theorem and its theorem
The diameter perpendicular to the chord bisects the chord and bisects the two arcs subtended by the chord.
The diameter that bisects the chord (not the diameter) is perpendicular to the chord and bisects the two arcs subtended by the chord
Use the vertical diameter theorem and its converse theorem to perform relevant calculations and proofs
Most of the auxiliary lines used in solving problems are used as radius
If two chords in a circle are parallel, then the arc between them is equal to the chord.
round
dr relationship
Three relationships between points in a circle
When d<r, the point is inside the circle
When d=r, the point is on the circle
When d>r, the point is outside the circle
Equal circles
Two circles with equal radii are called equal circles. Two equal circles can overlap
radius r
diameter
The chord passing through the center of the circle is called the diameter
Understand the concept of equal circles
definition
The fixed point is the center of the circle, and the fixed length is the radius. A circle with point O as the center is denoted as ⊙O and pronounced as "circle O"
It can be understood through the three lines of an isosceles triangle.
Properties and their inferences