In order for the trapezoid vertices to lie on the circle, the trapezoid must be symmetrical about the dotted line, which passes through the center of the circle. By drawing this vertical and the radii to points B and C we have created two right triangles, allowing us to use the Pythagorean Theorem. In fact, we might play an educated hunch that the triangles are 3–4–5 common right triangles. This checks out: If hypotenuse r is 5, then each triangle has a 3 and 4 side. The unknown vertical sides are

thus 4 and 3, which sum to 7 as they must. Algebraically, we can set up the following equations from the picture:

x^2 + 3^2 = r^2

y^2 + 4^2 = r^2

x + y = 7

Setting the two equations for r2 equal:

x^2 + 3^2 = y^2 + 4^2

x^2 – y^2 = 4^2 – 3^2

(x + y)(x – y) = 7

Since (x + y)(x – y) = 7, (x – y) = 1.

Solve for x and y:

(x + y) = 7

(x – y) = 7

2x = 8

x = 4

y = 7 – x = 3

The radius of the circle is 5, because r^2 = 3^2 + 4^2 = 25.

The correct answer is B.

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Thanks & Regards,

Anaira Mitch