In parallelogram ABCD, the length of the diagonal BD is equal to 5, the angle C = 60

In parallelogram ABCD, the length of the diagonal BD is equal to 5, the angle C = 60, the circle circumscribed about the triangle ABD touches the straight line CD. find the perimeter of the parallelogram.

Since point D lies on the circle, like the side of the triangle AВD, and the segment СD touches the circle, point D is the point of tangency between the circle and the segment СD.

Then СD and BC are tangent circles drawn from one point, and therefore BC = СD.

In the ВСD triangle, the angle is C = 60, ВС = СD, then the ВСD triangle is equilateral, ВС = СD = ВD = 5 cm, and the AВСD parallelogram is a rhombus.

Then Ravsd = 4 * BC = 4 * 5 = 20 cm.

Answer: the perimeter of the parallelogram is 20 cm.