Triangle in Triangle

Geometry Level 5

Find The maximum possible perimeter of an triangle ( XYZ ) which is inscribed in an another acute angled Triangle( ABC ). And It is given that circum-radius of outer Triangle is R

DETAILS AND ASSUMPTIONS

∙ \bullet Inner Triangle XYZ (as shown above) must touches the all 3 sides Of Outer Triangle ABC

∙ \bullet Use R=1


The answer is 5.196.

Deepanshu Gupta by Deepanshu Gupta , 25, India

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1 solution

Maximum possible perimeter is for the triangle itself. Hence we go equilateral and find the answer, which is 3 ( 3 ) 0.5 = 5.196 3(3)^{0.5}=\boxed{5.196}

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Yes , But You Have To Prove it , that outer triangle is equilateral , that's is also main part.

Deepanshu Gupta - 6 years, 3 months ago

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