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1953 AMC 12 Question 28

AMC12 · 1953 AMC 12

Question 28

In triangle $ABC,$ sides $a,$ $b$ and $c$ are opposite angles $A,$ $B$ and $C$ respectively. $\overline{AD}$ bisects angle $A$ and meets $\overline{BC}$ at $D.$ Then if $x=CD$ and $y=BD$ the correct proportion is:
  1. $\dfrac xa=\dfrac a{b+c}$
  2. $\dfrac xb=\dfrac a{a+c}$
  3. $\dfrac yc=\dfrac c{b+c}$
  4. $\dfrac yc=\dfrac a{b+c}$
  5. $\dfrac xy=\dfrac cb$