Problem 346. Equal circles, Tangents, Hexagon, Semiperimeter.
Level: High School, College, SAT Prep.
The figure shows equal circles A, B,
and C. AA1 and CC1
are tangents to circle B, AA2 and BB1 are
tangents to circle C, and BB2 and CC2 are
tangents to circle A. Points D, E, F, G, H, and M are the
intersection points of the tangents AA1 with BB2,
with CC1, BB1 with CC1, BB1
with AA2, CC2 with AA2, and CC2
with BB2, respectively. If s is the semiperimeter of
the hexagon DEFGHM, prove that s = DM+EF+GH = DE+FG+HM.
Geometry problem solving
Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."