I know the solution to this question but I need help. I want to know why was a construction done to the two triangles. What was the logic behind the construction? Or is there any other method to solve this question other than my method?

I know the solution to this question but I need help. I want to know why was a construction done to the two triangles. What was the logic behind the construction? Or is there any other method to solve this question other than my method?

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