Recently, with thanks to the folks at JSTOR who have made many of the older issues of The American Mathematical Monthly available without subscription, I have been reading through some of the early issues.
This morning I came across two interesting circle problems that looked both interesting, and challenging to the typical High School student, so here they are. I will wait a couple of days and post the answers.
18. Proposed by L. B. HAYWARD Superintendent of schools Bingham, Ohio:
In a circle whose radius is 6, find the area of the part between parallel chords
whose lengths are 8 and 10, both being on the same side of the center.
17. Proposed by H. W. HOLYCROSS, Superintendent of Schools, Pottersburg Union County, Ohio:
A gentleman owns a circular farm, and if three circles of equal area and as
large as possible be drawn within it, the circular area in the center of the farm will
contain one acre; what is the area of the circular farm ?