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Practice
Intercept Theorem

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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.

Solution:
The lines AB and CD are parallel, so by the intersect theorem, we have [tex]\frac{OB}{BD}=\frac{OA}{AC}[/tex], or [tex]OB=\frac{OA}{AC}.BD=\frac{6}{3}.1=2[/tex]. OD=OB+BD=2+1=3.

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.

Solution:
The lines AB and CD are parallel, so by the intersect theorem, we have [tex]\frac{OD}{OB}=\frac{CD}{AB}[/tex], or [tex]OD=\frac{CD}{AB}.OB=\frac{8}{6}.12=16[/tex]. BD=OD-OB=16-12=4.

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