A circle is inscribed into the trapezoid, the sum of the lengths of the sides of which is 34
| April 25, 2021 | education
A circle is inscribed into the trapezoid, the sum of the lengths of the sides of which is 34, find the middle line of the trapezoid.
Let us use the property of a trapezoid into which a circle is inscribed.
A circle can be inscribed into a trapezoid only if the sums of the opposite sides of the trapezoid are equal to each other.
AB + CD = AD + BC = 34.
The middle line of a trapezoid is equal to half the sum of the lengths of the bases of the trapezoid.
KM = (AD + BC) / 2 = 34/2 = 17 cm.
Answer: The middle line of the trapezoid is 17 cm.
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