Latest Maths Olympiad Aptitude Question SOLUTION: Let ABCDEF be a convex hexagon in which the diagonals AD, BE, CF are concurrent at O. Suppose the area of traingle OAF is the geometric mean of those of OAB and OEF; and the area o

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Previous Question: Find all pairs (x, y) of real numbers such that 16x^2 + y + 16x + y^2 = 1. Next Question: Let P1(x) = ax^2 + bx + c, P2(x) = bx^2 + cx +a, P3(x) = cx^2 + ax + b be three quadratic polynomials where a, b, c are non-zero real numbers. Suppose there exists a real number such that P1() = P2() = P3(). Prove that a = b = c.

(#M40021981) MATHS OLYMPIAD question GEOMETRY Keep an EYE

Let ABCDEF be a convex hexagon in which the diagonals AD, BE, CF are concurrent at O. Suppose the area of traingle OAF is the geometric mean of those of OAB and OEF; and the area of triangle OBC is the geometric mean of those of OAB and OCD. Prove that the area of triangle OED is the geometric mean of those of OCD and OEF.: Asked In Maths Olympiad MAN (11 years ago); Unsolved; Is this Puzzle helpful? (0) (1) Submit Your Solution

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Previous Question: Find all pairs (x, y) of real numbers such that 16x^2 + y + 16x + y^2 = 1. Next Question: Let P1(x) = ax^2 + bx + c, P2(x) = bx^2 + cx +a, P3(x) = cx^2 + ax + b be three quadratic polynomials where a, b, c are non-zero real numbers. Suppose there exists a real number such that P1() = P2() = P3(). Prove that a = b = c.

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