The lateral side of an isosceles trapezoid is 5 cm, the radius of a circle inscribed in it is 2 cm. Find the bases of the trapezoid.
| February 26, 2021 | education
The height of the trapezoid is equal to the diameter of the inscribed circle. BH = 2 * r = 4 cm.
In a right-angled triangle ABН, according to the Pythagorean theorem, AH^2 = AB^2 – BH^2 = 25 – 16 = 9. AH = 3 cm. Then DM = AH = 3 cm, since the trapezoid is isosceles.
Since a circle is inscribed in the trapezoid, AB + SD = BC + AD = 10 cm.
BC = НM, then BC + BC + AH + DM = 10 cm.
2 * BC = 10 – 3 – 3 = 4 cm.
BC = 2 cm, then AD = 2 + 6 = 8 cm.
Answer: The lengths of the bases are 2 cm and 8 cm.
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