In a 4-gon, each side has a length of either 6 or 8, and one of the diagonals is 10. What is the radius of the circumscribed circle?

According to the specification, one of the diagonals of the quadrangle is equal to 10 conventional units. That is, a triangle, where it is one of the sides, has dimensions: 6, 8 and 10 conventional units, respectively.

As we know from the inverse Pythagorean theorem, if the sum of the squares of the lengths of two sides is equal to the square of the length of the third, then it, a triangle, will be rectangular.

Let’s check:

√ (6 ^ 2 + 8 ^ 2) = √ (36 + 64) = √100 = 10.

10 = 10.

That is, our shape is a rectangle.

Let’s find out the radius of the circle:

10: 2 = 5.

Answer: 5 conventional units.