Inscribed circle radius formula, what is the universal formula for inscribed circle radius?

The radius of the inscribed circle of a right-angled triangle r=(a+b-c) 2, where a and b are the length of the right-angled side and c is the length of the hypotenuse.

General triangle: r=2s (a+b+c), where s is the area of the triangle and a, b, and c are the three sides of the triangle. In addition, s = p(p-a)(p-b)(p-c) under the root number, where p=(a+b+c) 2

Right triangle: The radius of the inscribed circle is r (a b c) 2

a, b is the right-angled edge, c is the hypotenuse) general triangle: the radius of the inscribed circle is r 2s (a b c).

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 the polygon is called a circle inscribed polygon. It is also the largest circle inside a polygon. The center of the inscribed circle is called the inner part of the polygon.

A polygon has at most one inscribed circle, i.e. for a polygon, its inscribed circle, if it exists, is unique. Not all polygons have inscribed circles. Triangles and regular polygons must have inscribed circles.

A quadrilateral with an inscribed circle is called a circular circumscribed quadrilateral.

Extended Materials. Nature:

1) In a triangle, the intersection of the angular bisector of the three corners is the center of the inscribed circle, and the perpendicular segments from the center of the circle 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 in the center of the regular polygon.

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

The formula for the radius of the inscribed circle is r=(a+b-c) 2 (a, b is the right-angled edge, c is the hypotenuse).

Right triangle: The radius of the inscribed circle is r (a b c) 2 (a, b is the right-angled edge, c isBeveled edgesGeneral triangle: the radius of the inscribed circle is r 2s (a b c).

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 the polygon is called a circle inscribed polygon. It is also the largest circle inside a polygon. The center of the inscribed circle is called the inner part of the polygon.

A polygon has an inscribed circle at most, that is, for a polygon, its inscribed circle, if it exists, is unique. Not all polygons have inscribed circles. Triangles and regular polygons.

There must be inscribed circles. A quadrilateral with an inscribed circle.

It is known as a circular outward quadrilateral.

Scalloped inscribed circle:

The circle tangent to the circle AB and the two radii OB and OB are called the inscribed circle of the fan.

The inscribed center of the circle o is bisector of the angle of the aob in the center of the circle of the fan.

Above. oo = r-r (r is the radius of the fan, r is the radius of the inscribed circle).

Over o as o a oa, perpendicular foot a, right triangle oao in.

o′oa=30°,o′a=r,oo′=r-r。

r=(r-r)*sin30°,r=1/2(r-r),r=3r。

Inscribed circle area.

r^2。

Find the radius formula for the inscribed circle: r=2s c. A circle tangent to all sides of a polygon is called an inscribed circle of a polygon. In particular, a circle tangent to all three sides of a triangle is called an inscribed circle of a triangle.

The center of the circle is called the inner part of the triangle, and the old shape of the triangle is called the circumscribed triangle of the circle. The heart of the triangle is the bisector of the three corners of the triangle.

of the intersection. In classical geometry, the radius of a circle or circle is any line segment from its center to its perimeter, and in more modern use, it is also the length of any of them. The name comes from the Latin radius, which means ray, and is also the spokes of a chariot.

The plural of radius can be radius (Latin.

plural) or regular English plural radius. The typical abbreviation for radius and the name of the mathematical variable is stupid r. By extension, the diameter d is defined as twice the radius: d = 2r.

The formula for the inscribed circle is r=2s (a+b+c).

The derivation process is as follows:

Divide the area of the large triangle ABC into three smaller triangles, i.e., OAB, 0BC, OAC.

then S ABC=S OAB+S 0bc+S Lifting Min OAC.

From the nature of the tangent [the distance between the tangent and the center of the circle is equal to the radius of the circle], it can be obtained:

OE, OF, and OG are the radii of the circle, that is, the three line segments marked with r in the figure.

From the nature of the tangent [the tangent is perpendicular to the radius passing through the tangent], it can be obtained:

oe⊥ab；og⊥bc；of⊥ac。

The formula for the area of a known triangle is: s = base length height 2

Let ab=c; bc=a；ac=b；Then:

s△oab=ab×r÷2= c×r÷2。

s△0bc= bc×r÷2=a×r÷2。

s△oac= ac×r÷2= b×r÷2。

i.e. s abc = c r 2+ a r 2+ b r 2 = ( c r + a r + b r ) 2.

That is, 2s = r (a + b + c) and r = 2s (a + b + c).

If the triangle ABC is a right-angled three-regular branch, the radius of the inscribed circle is r=(a+b-c) 2.

The derivation process is as follows:

The formula for the area of a known triangle is: s = base length height 2

Let ab=c; bc=a；ac=b；Then: s oab = ab r 2= c r 2,, s 0bc= bc r 2=a r 2, answer false.

s△oac= ac×r÷2= b×r÷2，s△abc=ac×bc÷2= b×a÷2。

Known S abc = S oab+s 0bc+s oac, s abc = b a 2, s oab + s 0bc + s oac = c r 2+ a r 2+ b a 2 = (a + b + c) r 2.

then, b a 2 = (a + b + c) r 2, then, r = (b a) a + b + c).

Since abc is a right-angled triangle, the Pythagorean law of a right-angled triangle: a+b=c, then, c= a+b=(a+b)-2ab, then, (a+b)- c=2ab, then, ab=[(a+b)- c] 2.

According to the previous r=(b a) (a+b+c), then r=[(a+b)-c] 2 (a+b+c)=(a+b+c)(a+b-c) 2 (a+b+c)= a+b-c) 2.

The formula for the radius of the inscribed circle of a right triangle: r=(a+b-c) 2

Let RT ABC, C 90 degrees, BC A, AC B, AB C

The conclusion is that the radius of the cutting circle of the inner mill is r (a b c) 2

There are generally two ways to prove this:

Let the center of the inscribed circle be O, and the three tangent points are D, E, and F, and connect OD and OE

Apparently there is od ac, oe bc, od oe so the quadrilateral cdoe is a square.

So cd ce r so ad b r, be a r, celery.

Because ad af, ce cf so af b r, cf a r

Because af cf ab r so b r a r r inscribed circle radius r (a b c) 2

That is, the diameter of the inscribed circle l a b c

Meaning. Right triangle: divided into two cases, there are ordinary right triangles, and isosceles right triangles (special cases) In the right angle triangle shape, the two sides adjacent to the right angle are called right angles, and the sides opposite the right angles are called hypotenuses.

The sides of a right triangle are also called "chords". If the two right-angled sides are not the same length, the short side is called the "hook" and the long side is called the "strand".