In this figure our aim is to find radius of the circle.
Note that only $4$ vertices of rectangles are on the circle.
My try: Since the top rectangle side and bottom rectangle side are parallel, From the diagram the distance between these parallel lines is $36$
Let $O$ be the center of the circle which is not known in the diagram.
If $OM$ is perpendicular drawn to top rectangle side and $ON$ is perpendicular drawn to bottom rectangle side then its evident that:
$$OM+ON=36 \tag{1}$$
Let the radius of the circle be $R$
we have a well know formula that length of the chord is given by
$$L=2\sqrt{R^2-x^2}$$ where $x$ is perpendicular length from center to the chord.
So length of bottom rectangle side is $30$ hence
$$2\sqrt{R^2-ON^2}=30 \tag{2}$$
Like wise
$$2\sqrt{R^2-OM^2}=10 \tag{3}$$
Solving $(1)$, $(2)$ and $(3)$ we get $$R=21.37$$
Is this fine?
Best Answer
Use the chord theorem of the circle to establish $ 10\cdot20=36\cdot x$. Then, the radius is
$$\sqrt{ \left(\frac{36+x}2\right)^2+ 5^2 } = \sqrt{ \left(\frac{36+\frac{50}9}2\right)^2+ 5^2 } = \frac{\sqrt{36994}}9=21.37 $$
which verifies your result.