A trapezoid is inscribed in a circle of radius 29, the bases of which are 40 and 42, and the center of the circle lies outside the trapezoid. Find the height of this trapezoid.
In a right-angled triangle OHD, according to the Pythagorean theorem, we determine the length of the leg OH.
OH ^ 2 = OD ^ 2 – D ^ 2 = 841 – 441 = 400.
OH = 20 cm.
In a right-angled triangle OCK, by the Pythagorean theorem, we determine the length of the leg OC.
OK ^ 2 = OC ^ 2 – CK ^ 2 = 841 – 400 = 441.
OK = 21 cm.
Then HC = OK – OH = 21 – 20 = 1 cm.
Answer: The height of the trapezoid is 1 cm.
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