The side of the rhombus is 25 cm, the smaller diagonal is 14 cm. Find the radius of the circle inscribed in the rhombus.

univerkov | February 26, 2021 | education

The diagonals of the rhombus are halved at the intersection and intersect at right angles. Then DO = ВD / 2 = 14/2 = 7 cm.

In a right-angled triangle AOD, according to the Pythagorean theorem, AO ^ 2 = AD ^ 2 – OD ^ 2 = 625 – 49 = 576. AO = 24 cm.

Then AC = 2 * AO = 2 * 24 = 48 cm.

Then R = AC * ВD / 4 * AD = 14 * 48/4 * 25 = 6.72 cm.

Answer: The radius of the inscribed circle is 6.72 cm.

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