A circle is inscribed in an isosceles trapezoid ABCD with bases AB = 7 and CD = 5.

| February 19, 2021 | education

A circle is inscribed in an isosceles trapezoid ABCD with bases AB = 7 and CD = 5. From point C the height CH is drawn, and from point H the perpendicular HE to the side BC. Find CE.

Since the circle is inscribed in the trapezoid, the sums of the sides of the trapezoid are equal.

AB + CD = AD + BC.

12 = AD + BC, and since the trapezoid is isosceles, then AD= BC = 12/2 = 6 cm.

The height of the CH divides the base AB into two segments, the length of the smaller of which is equal to: BH = (AB – CD) / 2 = (7 – 5) / 2 = 1 cm.

The segment EH is the height of the right-angled triangle CBH, drawn to the hypotenuse, then:

ВН ^ 2 = BC * BE.

BE = BH ^ 2 / BC = 1/6 cm.

Then CE = BC – BE = 6 – 1/6 = 35/6 = 5 (5/6) cm.

Answer: The length of the CE segment is 5 (5/6) cm.



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