Question (5): Let ABC be an arbitrary triangle in the plane. We define new points A', B',C' as in the figure such that BA = 5BC', AC = 5AB',CB = 5CA'. Denote by PQR the triangle (as in the figure below) formed by the intersections of the lines (AA'), (CC'), (BB'). Show %3D %3D that 3 times the area of the triangle ABC is always equals to 7 times the area of the triangle PQR. (Hint: Consider the problem first with an equilateral triangle ABC with side length 5 and then generalize). A' B'

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A:

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A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

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A: The section between points A and D is called

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