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

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

Aug 9, 2020

#1
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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.

Aug 10, 2020
#2
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Right scalene Pythagorean triangle.
Sides: a = 6 b = 8 c = 10

Area: T = 24
Perimeter: p = 24
Semiperimeter: s = 12
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

Aug 10, 2020
#3
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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.  62 + 82 = 102

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