Puzzle No. 011
Picarats: 20


As shown in the diagram below, you have one-forth of a circle. Within this circle is rectangle ABCD, which touches the edge of the circle at Point D.

Assuming that Point B is located at the center of the circle, how long is diagonal line AC?














Hint One: Surely somebody must have looked at the diagram and realized that the triangle formed by Points A, B, and C is a right triangle.

That's sharp thinking and exactly right. However, are you sure there isn't a much easier way to find the answer?

Hint Two: You don't need the Pythagorean theorem to answer this one. Something else in the diagram should be the exact same length as AC.

Hint Three: Notice that diagonal line AC within the rectangle is the same size as the diagonal line BD.

Have you also noticed that BD is also the same length as another part of this diagram?

Solution:













Righto! Diagonal line AC is the exact same length as diagonal line BD. BD is the same length as the radius of the circle, so once you've figured that out, the only thing left to do is add five and five.