Seven Problems in Equilateral Triangle

The following has been communicated to me in private correspondence by Emmanuel Antonio José García (15 February, 2014).

The basic configuration consists of an equilateral triangle with the base extended to twice its length:

Basic configuration of equilateral triangle with one side extanded

The statements appear as dashed lines; the lines that look tangent to a circle are indeed tangent. Solutions are welcome.

Problem 1

Problem 1 in equilateral triangle with one side extanded

Solution

Problem 2

Problem 2 in equilateral triangle with one side extanded

Solution

Problem 3

Problem 3 in equilateral triangle with one side extanded

Solution

Problem 4

Problem 4 in equilateral triangle with one side extanded

Solution

Problem 5

Problem 5 in equilateral triangle with one side extanded

Solution

Problem 6

Problem 6 in equilateral triangle with one side extanded

Solution

Problem 7

Problem 7 in equilateral triangle with one side extanded

Solution


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