A rectangle is inscribed in a circle with a radius of 25 cm, one side of which is 14 cm
| September 27, 2021 | education
A rectangle is inscribed in a circle with a radius of 25 cm, one side of which is 14 cm. Find the area of the rectangle. the answer should be 672cm2.
The diagonal BD of the rectangle passes through the center of the circumscribed circle and is equal to its diameter, then BC = 2 * OB = 2 * R = 2 * 25 = 50 cm.
From the right-angled triangle ВСD, according to the Pythagorean theorem, we determine the length of the leg СD.
CD ^ 2 = BD ^ 2 – BC ^ 2 = 2500 – 196 = 2304.
СD = √2304 = 48 cm.
Determine the area of the rectangle.
Savsd = ВС * СD = 14 * 48 = 672 cm2.
Answer: The area of the rectangle is 672 cm2.
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