What is the circumradius of a triangle ABC with sides of length 6,8,and 10?

Guest Aug 9, 2020

#1**+1 **

The circumcenter of a right triangle occurs at the midpoint of the hypotenuse.

The radius of the circumcircle will be the distance from the midpoint to either end of the hypotenuse;

in this case, the radius is 5.

geno3141 Aug 10, 2020

#2**+1 **

Right scalene Pythagorean triangle.

Sides: a = 6 b = 8 c = 10

Area: T = 24

Perimeter: p = 24

Semiperimeter: s = 12

Circumradius(R)

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. Circumcenter (center of circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

**R=(abc) / 4rs =6.8.10 / 4.2.12 =5 **

Guest Aug 10, 2020

#3**+1 **

*What is the circumradius of a triangle ABC with sides of length 6,8,and 10?*

We recognize that a 6, 8, 10 triangle is a right triangle. 6^{2} + 8^{2} = 10^{2}

Since it's a right triangle, the hypotenuse is the diameter of the circle it's inscribed in.

The radius is half the diameter, so .... **radius = 5**

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Guest Aug 10, 2020