A circle is inscribed in an isosceles trapezoid that divides the side into 6-inch and 8-inch segments, find the base.

univerkov | February 13, 2021 | education

Draw the segments OH, OK, OM to the points of tangency of the circle and the sides of the trapezoid.

By the property of tangents, drawn and one point, the lengths of the tangents are equal. Then AM = AH = 8 cm, ВK = BH = 6 cm.

Since the trapezoid is isosceles, the points of contact divide the sides into two groups of equal segments.

Then ВK = СK = 6 cm, AM = DM = 8 cm.

The length of the smaller base is equal to: BC = ВK + СK = 6 + 6 = 12 cm.

The length of the larger base is: AD= AM + DM = 8 + 8 = 16 cm.

Answer: The lengths of the bases of the trapezoid are 12 cm and 16 cm.

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