What is the length of the radius PQ?

Question

Answer 1

We know that PQ = r

We can use either the Pythagorean theorem or the understanding of a 3-4-5 triangle to evaluate r.

Let us call the mid-point of string QM "H":

1. we know that QH = HM because H is the mid-point,
2. we know that QM = 24
3. So QM = QH + HM = QH + QH = 2*QH ----> 24 = 2*QH ----> QH = 12

Now, we have 2 of the 3 sides of our right triangle.

1. to use the Pythagorean theorem we know that c = squareroot (a^2 + b^2 ), where c = r.
2. Plugging in we see that r = squareroot (12^2 + 9^2) = squareroot ( 144 + 81) = squareroot (225) = 15
3. to use 3-4-5
4. We know that 3*3 = 9
5. And that 3*4 = 12
6. And therefore the third side of our right triangle must be 3 * 5 = 15