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1950 AMC 12 Question 49

AMC12 · 1950 AMC 12

Question 49

A triangle has a fixed base $AB$ that is $2$ inches long. The median from $A$ to side $BC$ is $1\dfrac12$ inches long and can have any position emanating from $A.$ The locus of the vertex $C$ of the triangle is:
  1. A straight line $AB,$ $1\dfrac12$ inches from $A$
  2. A circle with $A$ as center and radius $2$ inches
  3. A circle with $A$ as center and radius $3$ inches
  4. A circle with radius $3$ inches and center
    $4$ inches from $B$ along $BA$
  5. An ellipse with $A$ as focus