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

bystudin | 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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