[Math] Determine the area of the right triangle AB'C' contained in the larger one ABC

Draw a right triangle ABC with sides AB and AC of length 3 and 4 respectively. Let B′ and C′ be two points belonging, respectively, to sides AB and AC, such that the line containing the segment B′C′ is parallel to that containing the hypotenuse BC and 1 distant from it.
Calculate the area of the triangle AB′C′.
Let's see how it's done.
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► The problem was taken from the 2005 math Olympics competition.
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