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math challenge II A geometry 4.29

 
 
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Re: math challenge II A geometry 4.29
by John Lensmire - Thursday, 30 September 2021, 12:49 PM
 

You already have that the RHS (right-hand side) of your expression, abc/(4R) is one way to calculate the area of the triangle.

Thus you can focus on the LHS. Here's a hint for there. The (s-a)(s-b)(s-c) reminds us of something we recognize from Heron's formula, except Heron's formula has an extra s in front. What happens if we multiply the numerator and denominator of that side by s?