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# Circumcircles/incircles

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I recently learned about circumcircles, incircles, circumradius, inradius, etc, but I don't really understand overall how to find them. Say I had a triangle with sides 10, 24, and 26. How would I calculate each of the above? An explanation would really help because I just don't understand how these are calculated. Thank you.

Jul 22, 2020
edited by gwenspooner85  Jul 22, 2020

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1)   Find the perimeter         P = a + b + c

2)   Find semiperimeter       s = ( a + b + c ) / 2

3)   Find area                       A = sqrt [ s( s-a )( s-b )( s-c )]       ( Heron's formula )

4)   Calculate inradius          r = A / s

5)    Calculate circumradius     R = ( abc ) /4rs

6)    Inner angles                    a2 = b2 + c2 - 2bc * cos(A)         ( The law of cosines )

I hope it covers everything you wanted to know. Jul 22, 2020
edited by Dragan  Jul 22, 2020
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Oh okay thank you, it helped me. For finding area of circumcircles and incircles, then you would just use the circumradius and inradius formulas to the find the radius, and continue on with the circle area formula correct?

gwenspooner85  Jul 22, 2020
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Yes! If you need to find the area of an incircle, you need only a radius of that circle. But if you need to find the area of a circumcircle, you need to find the lengths of both radii. Dragan  Jul 23, 2020
edited by Dragan  Jul 25, 2020
#4
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okay, thank you!

gwenspooner85  Jul 23, 2020