Saturday, June 24, 2023

Geometry Problem 1545: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters

Geometry Problem 1545. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Geometry Problem 1545: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters
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1 comment:

  1. Sumith PeirisJune 25, 2023 at 3:46 AM

    Let s = semiperimeter and S the area of Triangle ABC

    With the usual notation exradius rA = S /(s-a), BE = s-b

    Hence S(BEH) = (1/2)(S/(s-a))(s-b) = 11 so
    (s-b)/(s-a) = 22/S

    Simlarly (s-a)/(s-c) = 20/S and

    (s-c)/(s-b) = 12/S

    Multiplying, 1 = 22 X 20 X 12 / (S^3)
    Hence S = 2.(660)^(1/3) = 17.41 approximately

    Sumith Peiris
    Moratuwa
    Sri Lanka

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