A regular pentagon has sides of 10 cm. Find the radius of the largest circle which can be drawn inside the pentagon.

Panoptik asked Apr 18, 2022

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A regular pentagon has sides of 10 cm. Find the radius of the largest circle which can

be drawn inside the pentagon.

Panoptik asked Apr 18, 2022

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24 votes

Answer is 6.88 cm

Divide the pentagon radially into five congruent, isosceles triangles. Each triangle has a vertex angle of 360°÷5=72° and altitude of 5÷tan(36°).

radius of circle = 5÷tan(36°) = 6.88 cm

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