MathDB

6

Part of 2015 Regional Olympiad of Mexico Center Zone

Problems(1)

\pi (a + b + c)^2 <=12T

Source: Mathematics Regional Olympiad of Mexico Center Zone 2015 P6

11/12/2021
We have 33 circles such that any 22 of them are externally tangent. Let aa be length of the outer tangent common to a pair of them. The lengths bb and cc are defined similarly. If TT is the sum of the areas of such circles, show that π(a+b+c)2≤12T\pi (a + b + c)^2 \le 12T .
Note: In In the case of externally tangent circles, the common external tangent is the segment tangent to them that touches them at different points.
geometryGeometric Inequalities