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Midpoint of Line Segment

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February 7, 2009
geometrysimilar triangles

Problem Statement

The locus of the midpoint of a line segment that is drawn from a given external point P P to a given circle with center O O and radius r r, is: <spanclass=′latex−bold′>(A)</span> a straight line perpendicular to PO‾<spanclass=′latex−bold′>(B)</span> a straight line parallel to PO‾<spanclass=′latex−bold′>(C)</span> a circle with center P and radius r<spanclass=′latex−bold′>(D)</span> a circle with center at the midpoint of PO‾ and radius 2r<spanclass=′latex−bold′>(E)</span> a circle with center at the midpoint PO‾ and radius 12r <span class='latex-bold'>(A)</span>\ \text{a straight line perpendicular to }\overline{PO} \\ <span class='latex-bold'>(B)</span>\ \text{a straight line parallel to } \overline{PO} \\ <span class='latex-bold'>(C)</span>\ \text{a circle with center }P\text{ and radius }r \\ <span class='latex-bold'>(D)</span>\ \text{a circle with center at the midpoint of }\overline{PO}\text{ and radius }2r \\ <span class='latex-bold'>(E)</span>\ \text{a circle with center at the midpoint }\overline{PO}\text{ and radius }\frac{1}{2}r
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