Circle's Corner

Consider the two lines AO and BO. These two lines intersect at point O and are perpendicular to each other.

If you were to draw a circle that were to intersect these two lines at points A and B and only at points A and B, what would be the smallest integral size of the larger arc AB in degrees?

181 ??

Answer

181 degrees.

If you created a circle with points A, B, and O on it, since angle AOB is a right angle, line AB is the diameter of this circle. Therefore, arc AB would be 180 degrees if it actually were to intersect O as well as A and B.

However, the problem says the arc can only intersect A and B. To do this, the circle must be slightly larger than the one described above. As stated in the problem, the larger arc must be the next largest integer size, which is 181 degrees.

i pulled out my old math book for this one!