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What is the circumradius of a triangle with sides 29, 29 and 42?

 Aug 9, 2023
 #1
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The circumradius of a triangle with sides of lengths a, b, and c is given by the formula

R = \frac{abc}{4\sqrt{(s)(s - a)(s - b)(s - c)}}

where s is the semiperimeter of the triangle, s = (a + b + c) / 2.

In this case, the sides of the triangle are 29, 29, and 42, so the semiperimeter is s = (29 + 29 + 42) / 2 = 49. The area of the triangle is then

A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{49(49 - 29)(49 - 29)(49 - 42)} = 420

Therefore, the circumradius is

R = \frac{abc}{4A} = \frac{(29)(29)(42)}{4(420)} = \frac{29}{6}

 Aug 9, 2023
 #2
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Calculation of  "inradius"
r ==Area / semi-perimeter
r==420 / 50
r ==8.4
Calculation of "circumradius"
R ==abc / [4 * inradius * semi-perimeter]
R==[29 * 29 * 42] / [4 * 8.4 * 50]
R ==21.03 - The circumradius

 Aug 10, 2023

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