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已知：平行四边形ABCD的对角线交点为O，点E、F分别在边AB、CD上，分别沿 DE、BF折叠四边形ABCD，A、C两点恰好在O点处，且四边形DEBF为菱形（如图）． （1）求证：四边形ABCD是矩形； （2）在四边形ABCD中，求 AB BC 的值．
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