In Olympiad geometry, lemmas are intermediate results or statements that are used to prove more complex theorems or solve challenging problems. These lemmas are often simple to state but require clever proofs, making them an essential part of the problem-solving process. Lemmas can be categorized into two types:
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In triangle ABC, the symmedian from A meets BC in a point D such that BD/DC = AB²/AC². Constructing the Lemoine point and solving ratio problems. In Olympiad geometry, lemmas are intermediate results or