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The sides of Traingle ABC have lengths sqrt10, sqrt10, and 2. What is the circumradius of Traingle ABC?

 Nov 15, 2019
 #1
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 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. Circumcenter (center of circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

 

R = { a b c } / { 4 r s } = { 3.16 * 3.16 * 2 } / { 4 * 0.721 * 4.162 } = 1.667, where r =inradius, s =semiperimeter.

 Nov 15, 2019
 #2
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Let

a, b  =  √10 

c = 2  

 

The circumradius can be found as

 

  (abc) / √((a + b + c)(b + c - a)(c + a - b)(a + b - c))

 

So we have

 

( 10*2) / √   [ ( 2√10 + 2) ( 2) ( 2 ) ( 2√10 - 2)  ]  =

 

20  /  √ [ (40 - 4) (4) ] = 

 

20 / √ [ 36 * 4]  =

 

20 / √144 =

 

20 /12  =

 

5/3   units

 

 

cool cool cool

 Nov 15, 2019
 #3
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+1

Thx Cphill

 Nov 15, 2019

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