(1) In a triangle, the intersection of bisectors of three angles is the center of the inscribed circle, and the vertical segments from the center to each side of the triangle are equal.

(2) A regular polygon must have an inscribed circle, and the center of the inscribed circle and the center of the circumscribed circle coincide, both at the center of the regular polygon.

(3) Common auxiliary lines: perpendicular to the center of the circle.

A triangle must have an inscribed circle, but other figures do not. The center of the inscribed circle is located inside the triangle.

Extended data:

For a general triangle, the triangle area formula is as follows: s=r(a+b+c)/2.

In the inscribed circle of the right triangle s=r(a+b+c)/2, there are two simple formulas as follows:

1, the sum of two right angles minus the hypotenuse and then divided by 2, the number is the radius of the inscribed circle: r=(a+b-c)/2.

(Note: S is the area of Rt△, A and B are the two right angles of Rt△, and C is the hypotenuse)

2. The product of two right-angled sides divided by the perimeter of a right-angled triangle is the radius of the inscribed circle: r=ab/ (a+b+c).