A rectangle is inscribed in a circle with a radius of 10 cm, one side of which is 14 cm. Find the area of the rectangle.
| February 26, 2021 | education
The diagonal of the ВD of the rectangle passes through the center of the circumscribed circle and is equal to its diameter, then BC = 2 * OB = 2 * R = 2 * 10 = 20 cm.
From the right-angled triangle of the ВСD, according to the Pythagorean theorem, we determine the length of the СD leg.
СD ^ 2 = ВD ^ 2 – BC ^ 2 = 400 – 196 = 204.
СD = √204 = 2 * √51 cm.
Determine the area of the rectangle.
Savsd = BC * СD = 14 * 2 * √51 = 28 * √51 cm2.
Answer: The area of the rectangle is 28 * √51 cm2.
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