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1963 AMC 12 Question 18

AMC12 · 1963 AMC 12

Question 18

Chord $EF$ is the perpendicular bisector of chord $BC,$ intersecting it in $M.$ Between $B$ and $M$ point $U$ is taken, and $EU$ extended meets the circle in $A.$ Then, for any selection of $U,$ as described, triangle $EUM$ is similar to triangle:

Question illustration
  1. $EFA$
  2. $EFC$
  3. $ABM$
  4. $ABU$
  5. $FMC$