Rectangle - parallelogram

A rectangle is circumscribed by a circle with a radius of 5 cm. The short side of the rectangle measures 6 cm. Calculate the perimeter of a parallelogram ABCD, whose vertices are the midpoints of the sides of the rectangle.

Correct answer:

o =  20 cm

Step-by-step explanation:

$$\begin{gathered} r=5\text{cm} \\ a=6\text{cm} \\ u=2\cdot r=2\cdot 5=10\text{cm} \\ {u}^2=a^2+b^2 \\ b=\sqrt{u^2-a^2}=\sqrt{10^2-6^2}=8\text{cm} \\ x=\sqrt{(a/2{)}^2+(b/2{)}^2}=\sqrt{(6/2{)}^2+(8/2{)}^2}=5\text{cm} \\ o=4\cdot x=4\cdot 5=20\text{cm} \end{gathered}$$

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