What is the center of an inscribed circle and what is the nature of an inscribed circle?

To compare the inner and outer mind, we must grasp the definition.

The heart is the center of the circle with the inscribed circle, that is to say, the circle is tangent to the three sides, and if the center of the circle is connected with the tangent point, then the distance from the center of the circle to the three sides is equal, that is to say, the heart is the intersection of the bisector of the angle.

The outer center is the center of the circumscribed circle, that is, the three vertices of the triangle are on the circumscribed circle, so the distance from the center of the circle to the three vertices is equal. So it is the intersection of the perpendicular bisectors of each side.

The rest of the properties can be excavated from here.

The so-called triangular"Four hearts", which refers to the intersection of the four important line segments of the triangle to form four types of special points. They are the inner center, outer center, vertical center and center of gravity of the triangle.

1.Perpendicular The height of the three sides of a triangle intersects at one point, which is called the vertical center of the triangle.

2.Center of gravity The center line of the three sides of the triangle intersects at one point, which is called the center of gravity of the triangle.

3.The perpendicular lines of the three sides of the triangle intersect at one point, which is the center of the circumscribed circle of the triangle, which is called the outer center.

4.The bisector of the three inner angles of the triangle intersects at one point, which is the center of the inscribed circle of the triangle, called the heart, and the intersection of the center of gravity on the three sides of the middle line.

Vertical center The intersection of three high points.

The inner circumscribed circle center is the intersection of the three angular bisector lines.

Outer Center Circumscribed Circle Center Intersection of the Perpendicular Bisector of the Three Sides The Intersection of the Perpendicular Bisector of the Three Sides of a Triangle!

The outer center of an acute triangle is inside the triangle;

The outer center of a right triangle is the midpoint of the hypotenuse;

The outer center of an obtuse triangle is outside the triangle!

The center of the circumscribed circle is the outer center, which is the intersection of the perpendicular bisector of each side, and the distance from the center of the circle to the three vertices is equal.

The intersection of the perpendicular bisector of the three sides of a triangle!

The outer center of an acute triangle is inside the triangle;

The outer center of a right triangle is the midpoint of the hypotenuse;

The outer center of an obtuse triangle is outside the triangle!

withPolygonsA circle where all the vertices intersect is called a polygonal oneCircumscribed circle

Triangles have circumscribed circles, and other shapes do not necessarily have circumscribed circles. The circumscribed circle center grip of the triangle is the perpendicular bisector of either side.

of the intersection. The center of the triangle circumscribed circle is called the outer center. Triangles have circumscribed circles, and other shapes do not necessarily have circumscribed circles. The circumscribed center of a triangle is the intersection of the perpendicular bisector on either side. The center of the triangle circumscribed circle is called the outer center.

Nature:

Acute triangle outer center.

Inside the three-kidenier corner.

The outer center of the right triangle is on the hypotenuse of the triangle.

Midpoint. Obtuse angle.

The outer center of the triangle is outside the triangle.

A figure with an outer center must have an outer circle (the intersection of the perpendicular lines on each side is called the outer center).

The length of the line segments from the center of the circumscribed circle to the vertices of the triangle is equal.

The above content reference: Encyclopedia - external pulse skin scrambling circle.

The properties of the circumscribed circle are as follows:1. The outer center of an acute triangle.

Inside the triangle.

2. The outer center of the right triangle is on the hypotenuse of the triangle.

Midpoint. 3. Blunt angle.

The outer center of the triangle is outside the triangle.

4. There is an external center of the figure, there must be an external circle (the vertical line on each side.

is called the outer heart).

5. The length of the line from the center of the circumscribed circle to each vertex of the triangle is equal. Positive returns.

Drawing method: that is, make the vertical bisector of the three sides of the triangle.

Two can also be, the intersection of the two lines determines a point).

Take a line segment as an example, which can be seen as one side of a triangle. Make a circle with two endpoints as the center of the circle, the appropriate length (equal) as the radius (only draw the arc that intersects with the line segment), and then take the two intersection points as the center of the circle, and the equal length as the radius (to ensure that the two circles intersect) to make a circle, and make a straight line through the two intersection points of the last two circles, the straight line is perpendicular and bisects this line segment, that is, the vertical bisector of the line segment.

The properties of the circumscribed circle are as follows:1. The outer center of an acute triangle.

Inside the triangle. Shizi.

2. Right triangle.

The outer center is on the hypotenuse of the triangle.

Midpoint. 3. Obtuse triangle.

The outer center is outside the triangle.

4. There is a figure that lifts the heart of God, and there must be an external circle (perpendicular line on each side.

is called the outer heart).

5. The length of the line segments from the center of the circumscribed circle to each vertex of the triangle is equal.

6. The circle that passes through the three vertices of the triangle is called the circumscribed circle of the triangle, and its center is called the outer center of the triangle. In a triangle, the outer center of the triangle is not necessarily inside the triangle, but may be outside the triangle (e.g., an obtuse triangle) or on the edge of the triangle (e.g., a right-angled positive triangle).

7. Three points that are not on the same straight line can be made into a circle (and only one circle).

Drawing Method:That is, to make a perpendicular bisector of the three sides of the triangle.

Two can also be, the intersection of the two lines determines a point).

Take a line segment as an example, which can be seen as one side of a triangle. Make a circle with two endpoints as the center of the circle, the appropriate length (equal) as the radius (only draw the arc that intersects with the line segment), and then take the two intersection points as the center of the circle, and the equal length as the radius (to ensure that the two circles intersect) to make a circle, and make a straight line through the two intersection points of the last two circles, the straight line is perpendicular and bisects this line segment, that is, the vertical bisector of the line segment.

Circumscribed circleThe center of the circle is the perpendicular bisector of the three sides of the triangle.

of the intersection. The center of the triangle circumscribed circle is called the outer center. The concept of a perpendicular bisector is the only one that exists when a line segment exists. It is defined as a straight line that passes through the midpoint of a line segment and is perpendicular to that line segment, called the perpendicular bisector of the line segment (the perpendicular line).

It has certain limitations.

Axisymmetric graphics.

The axis of symmetry is the perpendicular bisector of any two corresponding point segments in a symmetry graph. The perpendicular bisector of the three sides of the triangle can be seen as one side of the triangle as an example. Make a circle with two endpoints as the center of the circle, and the appropriate length (equal) as the radius, and then take the two intersection points as the center of the circle, the equal length as the radius to make a circle, and make a straight line through the two intersection points of the last two circles.

1. Differences: 1. Inscribed and inscribed refers to the positional relationship of plane figures, and extrinsic is the relationship between three-dimensional geometric figures, while inscribed can be plane figures or pre-tour plexus is the positional relationship between three-dimensional geometric figures.

2. Inscribed and inscribed are the positional relationships between different plane figures and circles, and one of the figures must be a circle.

3. Circumference refers to the positional relationship between the ball and other three-dimensional geometric figures, and one of the figures must be a ball.

4. The external incision of regrets refers to the positional relationship between different geometric figures (plane or three-dimensional), and the external incision is more than that of the gods.

2. Introduction to various location relationships:

1. Internal incision. <>

Incision is when one of the circles is inside the other. And the two circles have one and only one intersection point. Note that the incut is talking about the positional relationship between circles.

2. External incision. <>

If each side of a polygon (or polyhedron) (or each side of a polyhedron) is tangent to a closed curve (or surface) located within it, the polygon (or polyhedron) is said to be tangent to the curve (or surface).

There are circle and circle incision, circle and polygon, sphere and sphere incision, sphere and polyhedral incision, and some other inscribed relations.

3. Internal connection. <>

If the vertices of a polygon are on the same circle, then the circle is called the circumscribed circle of the polygon, and the polygon is called the circumscribed polygon of the circle. is the relationship between the circle and the figures in the circle.

4. External. <>

The external sphere is broadly understood to mean that the ball surrounds the geometry, and the vertices and arcs of the geometry are on the ball.

Circles and inscribed circles are often called inscribed circles, and outer inscribed circles are called inscribed circles.

Inscribed circle: Usually one circle is for another circle, indicating the position of the two circles. If one circle is inside another great circle, and the two circles have only one common point, this circle is called a great circle, i.e., two circles inscribed.

The position relationship between the circle and the circle is divided into:

Alien, tangent (inscribed and inscribed), intersected, contained. In a plane, a closed curve formed by a moving point centered on a certain point and rotated around a certain length is called a circle.

There is no common point, a circle outside another circle is called alienation, and within it is called inclusion.

If there is a single common point, a circle outside another circle is called an outward incision, and an inner circle is called an incision.

There are two common points called intersection. The distance between the centers of two circles is called the center distance.

1 Circumscribed circle: The circle that intersects with all the vertices of the polygon is called the circumscribed circle of the polygon, usually for a convex polygon, such as a triangle, if a circle exactly passes three vertices, the circle is called the circumscribed circle of the triangle, and the circle just surrounds the triangle.

2. Inscribed circle: In mathematics, if each side of a polygon on a two-dimensional plane can be tangent to a circle inside it, the circle is the inscribed circle of the polygon, and this polygon is called a circle inscribed polygon. It is also the largest circle within the polygon.

The center of the inscribed circle is called the heart of the polygon cavity.

3. Inscribed circle: Usually for another circle, if a circle is inside another large circle, and the two circles have only one common point, this circle is called the inscribed circle of the great circle.

4. Inscribed circle: The inscribed circle is for another circle, if the two circles have only one common point, and the distance between the center of the circle is equal to the sum of the radii of the two circles, the two circles are inscribed circles to each other. When two circles are cut outward, there are 3 common tangent lines.