Answers

  • Brainly User
2015-12-31T04:06:02+08:00
There are two ways to find the radius of circumscribing circle of a triangle (triangle  inside the circle and whose three vertices are on the circle).

Choose one that you can easily remember:

Method A:
1.) Find the semi-perimeter (s) of the triangle, where a, b, and c are the sides         
     of the triangle:

     s = (a + b+ c) ÷ 2

2.)  Solve for the radius (r) given the semi-perimeter (s) of the triangle, and the      
      the sides a, b, and c:
 
     r =  \frac{abc}{4 \sqrt{s(s-a)(s-b)(s-c)} }

Solution using Method A:
a = 80 cm;  b = 100 cm;  c = 140 cm

Find the triangle's semi-perimeter: (half of the triangle's perimeter)

s = (80 + 100 + 140) ÷ 2

s = 320 cm ÷ 2

s = 160 cm


Solve for radius given the semi-perimeter (160 cm) and sides a, b, c:


r = (abc) ÷ 4 \sqrt{s(s-a)(s-b)(s-c)}

r =   \frac{(80cm)(100cm)(140cm)}{4 \sqrt{140cm(160cm-80cm)(160cm-100cm)(160cm-140cm)} }

r =  \frac{1,120,000cm ^{3} }{4 \sqrt{(160cm)(80cm)(60cm)(20cm)} }

r =  \frac{1,120,000cm ^{3} }{4 \sqrt{15,360,000cm ^{4} } }

r = \frac{1,120,000cm ^{3} }{4 (3,919.18cm ^{2})  }

r =  \frac{1,120,000cm ^{3} }{15,676.72cm ^{2} }

r ≈ 71.44 cm

ANSWER:  The radius of circumscribing circle is 71.44 cm.

Method B:

r =  \frac{abc}{ \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-a)} }

Substitute the given measurements of sides a, b and, c, then evaluate.
The result is the same.

       

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