Find the length of a circle circumscribed about a rectangle whose smaller side is 8 cm
| September 9, 2021 | education
Find the length of a circle circumscribed about a rectangle whose smaller side is 8 cm and the angle between the diagonals is a.
Since the quadrilateral ABCD is a rectangle, then its diagonals are equal and at the point of intersection they are divided in half, then OA = OB.
The AOB triangle is isosceles. Let’s construct the height OH, which is also the median and the bisector. Then the angle BON = α / 2, and BH = AB / 2 = 8/2 = 4 cm.
In a right-angled triangle ОВН, Sin (α / 2) = ВН / ОВ.
ОВ = ВН / Sin (α / 2) = 4 / Sin (α / 2) see.
The OB segment is the radius of the circumscribed circle, then the circumference is equal to:
L = 2 * π * ОВ = 8 * π / Sin (α / 2).
Answer: The circumference is 8 * π / Sin (α / 2).
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