A circle centered at the origin passes through the point (3, 4). What is the radius of the circle?

The radius is the distance from the center, the origin, to any point on the circle. Use the distance formula, or the Pythagorean theorem with legs 3 and 4: $r = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$. This is the familiar 3-4-5 right triangle. Equivalently, the circle is $x^2 + y^2 = 25$, which contains $(3,4)$ since $9 + 16 = 25$. A common wrong answer is 25, which is $r^2$, and another is 7, the sum of the coordinates. A third is 12, the product. The radius must be the square root of the sum of squares.