External mind is a mathematical term. Refers to the intersection of the median vertical lines (also called median vertical lines) of three sides of a triangle. With this point as the center, the circumscribed circle of the triangle can be drawn. Refers to the center of the circumscribed circle of a triangle, which is generally called the outer center of the triangle.
The outer center of a triangle is the intersection of the perpendicular lines of three sides, and the distance from this point to the three vertices of the triangle is equal. The epicenter is the intersection of the perpendicular bisector of the three sides of the triangle, which is the center of the circumscribed circle.
Property: the outer center of an acute triangle is inside the triangle. The outer center of a right triangle is located at the midpoint of the hypotenuse of the triangle. The outer center of an obtuse triangle is outside the triangle. A figure with an outer center must have a circumscribed circle (the intersection of vertical lines on each side is called an outer center blind guess). A circle whose line segment length from the center of the circumscribed circle to each vertex of the triangle is equal to the line segment length of the three vertices of the triangle is called a triangle circumscribed circle, 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 can be outside the triangle (such as an obtuse triangle) or on the side of the triangle (such as a right triangle). Passing three points that are not on the same straight line can make a circle (and there is only one circle).
The nature of the outer center of a triangle: the outer center of an acute triangle is inside the triangle; The outer center of the right triangle is on the hypotenuse and coincides with the midpoint of the hypotenuse; The outer center of an obtuse triangle is outside the triangle. The perpendicular lines of the three sides of a triangle intersect at a point, which is the center of the circumscribed circle of the triangle, and the distances from the outer center to the three vertices are equal.
The center of a triangle
1, center: The bisectors of three internal angles of a triangle intersect at a point, which is called the triangle center; The center of a regular triangle is called the center of the triangle, where the center of gravity, the center of gravity, the outer center and the inner center coincide.
2. A triangle corresponds to three vertices, each corner has a bisector, and the three lines intersect at * * *, which is called "inner heart" and has roots; The points to the three sides are equidistant, which can be used as a triangle inscribed circle. This center of the circle is naturally defined as the heart.