Help meee find the radius

Find the circumradius of triangle ABC. Find the inradius of triangle ABC.

3 4 5

5 12 13

4 5 6

8 8 8

19 19 40

3 3 4

13 14 15

1 2 3

23 40 55

6 8 10

19 20 21

Guest Jan 31, 2023

#1**0 **

11 Triangles !!!!!!!!!!!

I will do the first and you do the rest. Submit 1 question at a time.

3, 4, 5

Right scalene Pythagorean triangle.

Sides: a = 3 b = 4 c = 5

Area: T = 6

Perimeter: p = 12

Semiperimeter: s = 6

**Inradius**

An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.

T=rs, Where T==area, r==inradius, s==semi-perimeter.

r=T / s

**r = 6 / 6 ==1**

**Circumradius**

The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

R==(abc) / (4rs)

**R ==(3.4.5) / (4.1.6) ==2.5**

Guest Jan 31, 2023