In Euclid's geometry context, I have the following problem: Let ABC a triangle and P laying in AB. We need to find a point Q in AC or BC such that the triangle APQ has the half of the area of ABC. Let M be the medium point of AB. Construct a parallel segment to PC passing by M, and call Q it's intersection with AC (or BC). Prove that Q is the point we find.
Find a segment dividing a triangle in equal areas.
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geometry