state and prove ceva's theorem
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Ceva's theorem is a theorem about triangles in Euclidean plane geometry. It regards the ratio of the side lengths of a triangle divided by cevians. ... Ceva's theorem is useful in proving the concurrence of cevians in triangles and is widely used in Olympiad geometry.
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Ceva's Theorem states that given any triangle △ABC, the segments from A, B, and C to the opposite sides of the triangle are concurrent precisely when the product of the ratios of the pairs of segments formed on each side of the triangle is equal to 1.
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