# A circle is inscribed in the parallelogram. Find the perimeter of a parallelogram if one of its sides is 6

May 31, 2020 | Education

| A circle can be inscribed in a quadrangle when the condition is satisfied:

AB + CD = BC + AD

AB = CD = x (according to the parallelogram property)

BC = AD = y (by the parallelogram property)

We get:

x + x = y + y

2x = 2y

x = y, i.e. all sides of our parallelogram are equal, therefore it is a rhombus.

The perimeter of the rhombus is equal to:

P = 6 * 4 = 24

Answer: 24

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