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Posted on March 19, 2019March 19, 2019 by Gianni Sarcone

Sangaku: Semicircle inscribed in a right triangle

Find the radius r of the semicircle inscribed in the right triangle below:


show solutionhide solution

The altitude h of the right triangle is:
h = 6 ยท 8/10 = 4.8
By similarity:
4.8/r = 8/(8-r)
Thus
r = 3
CategoriesEquations, Geometry, Mathematics, Puzzle Tagsright triangle, sangaku, semicircle

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