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:

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

Problem 1

Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

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