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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

 Jan 31, 2023
 #1
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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

 Jan 31, 2023

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