# Find the radius of a circle inscribed in a trapezoid if its bases are 8 and 2.

An error was made in the problem statement. It is not indicated that the trapezoid is isosceles.

1. A, B, C, D – the tops of the trapezoid. AB = CD. BC = 2 units. AD = 8 units.

2. A circle can be inscribed in a trapezoid, provided that the sum of the lengths of the opposite sides are equal. That is, AB + CD = BC + AD.

Hence, AB = CD = (8 + 2) / 2 = 5 units.

3. Draw from the top B height BE to the base AD.

4. Calculate the length of the segment AE:

AE = (AD – BC) / 2 = (8 – 2/2 = 3 units.

5. We calculate the length of the height BE, using the Pythagorean theorem:

BE = √AB² – AE² = √5² – 3² = √25 – 9 = √16 = 4 units.

6. Calculate the radius of the circle (r), which is inscribed in the trapezoid:

r = BE / 2 = 4: 2 = 2 units.

Answer: the radius of the circle, which is inscribed in the trapezoid, is equal to 2 units.

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