MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Mathematical Competitions 131
Figure 5.3: AMC 1977
Problem 8 (AMC 1977). In Figure 5.3, each of the three circles is externally
tangent to the other two, and each side of the triangle is tangent to two of the
circles. If each circle has radius ρ then show that the perimeter of the triangle
is ρ · (6 + 6 √ 3). [11, p. 29]
Figure 5.4: AMC 1978
Problem 9 (AMC 1978). In Figure 5.4, if ∆A1A2A3 is equilateral and An+3
is the midpoint of line segment AnAn+1 for all positive integers n, then show
that the measure of ∠A44A45A43 equals 120 ◦ . [11, p. 39]