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1950 AHSME Problems/Problem 49

Revision as of 12:45, 18 January 2012 by Mrdavid445 (talk | contribs) (Created page with "==Problem== A triangle has a fixed base <math>AB</math> that is <math>2</math> inches long. The median from <math>A</math> to side <math>BC</math> is <math> 1\frac{1}{2}</math> ...")
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Problem

A triangle has a fixed base $AB$ that is $2$ inches long. The median from $A$ to side $BC$ is $1\frac{1}{2}$ inches long and can have any position emanating from $A$. The locus of the vertex $C$ of the triangle is:

$\textbf{(A)}\ \text{A straight line }AB,1\dfrac{1}{2}\text{ inches from }A \qquad\\ \textbf{(B)}\ \text{A circle with }A\text{ as center and radius }2\text{ inches} \qquad\\ \textbf{(C)}\ \text{A circle with }A\text{ as center and radius }3\text{ inches} \qquad\\ \textbf{(D)}\ \text{A circle with radius }3\text{ inches and center }4\text{ inches from }B\text{ along } BA \qquad\\ \textbf{(E)}\ \text{An ellipse with }A\text{ as focus}$

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