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1959 AMC 12 Question 2

AMC12 · 1959 AMC 12

Question 2

Through a point $P$ inside triangle $ABC$ a line is drawn parallel to the base $\overline{AB},$ dividing the triangle into two equal areas. If the altitude to $\overline{AB}$ has length $1,$ then the distance from $P$ to $\overline{AB}$ is:
  1. $\dfrac12$
  2. $\dfrac14$
  3. $2-\sqrt2$
  4. $\dfrac{2-\sqrt2}{2}$
  5. $\dfrac{2+\sqrt2}{8}$