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Intercept Theorem: Difficult Problems with Solutions

Problem 1
The line CD is parallel to AB and crosses the angle BOA so that O,B,D lie on the same line and so do O,A,C. If OA=6, AC=3 and BD=1, determine the length of OD.
Problem 2
The line CD is parallel to AB and crosses the angle BOA so that O,B,D lie on the same line and so do O,A,C. If AB=6, CD=8 and OB=12, determine the length of BD.
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