# Problem of the Day: 1/29/13

In the rhombus below, angles A and B are 120°, and C and D are 60°. If AC = 8 cm, what is the radius of the circle? Express your answer with simplified radicals.

Solution to yesterday’s problem:

To find the greatest common factor of two numbers, find the prime factorization of the numbers and multiply the factors that occur in both numbers. (This method contrasts with the least common multiple, in which we multiply all the factors except the ones that occur in both numbers. We multiply more numbers to get the LCM, the multiple.) Luckily for us, we already have the prime factorization!

The numbers are $2\times2\times2\times3\times5$ and $2\times2\times3\times3\times5\times5$. Notice that both numbers have at least 2 twos, 1 three, and 1 five. Multiplying these factors together, we have $2\times2\times3\times5$, which yields 60.