MathDB

70

Part of 1990 IMO Longlists

Problems(1)

Apolonius Theorem - ILL 1990 PRK4

Source:

9/18/2010
BCBC is a segment, MM is point on BCBC, AA is a point such that A,B,CA, B, C are non-collinear.
(i) Prove that if MM is the midpoint of BCBC, then AB2+AC2=2(AM2+BM2).AB^2 + AC^2 = 2(AM^2 + BM^2).
(ii) If there exists another point (except MM) on segment BCBC satisfying (i), find the region of point AA might occupy.
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