Question 6

(a) If a, b, c are positive real numbers such that no two of them are equal, show that $$a(a-b)(a-c) + b(b-c)(b-a) + c(c-a)(c-b)$$ is always positive. 

(b) In the figure below, P, Q, R, S are points on the sides of triangle ABC such that $$CP=PQ=QB=BA=AR=RS=SC$$.

image


Correct Answer: part_a=0 part_b=25.7142857143

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