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SMO 2012 Senior Round 1 Question 9

SMO · SMO 2012 Senior Round 1

Question 9

In triangle $ABC$, $AB=AC$, $\angle ABC=40^\circ$, and $D\in AC$ with $BD$ bisecting $\angle ABC$. Extend $BD$ beyond $D$ to $E$ with $DE=AD$. Find $\angle ECA$.

Question illustration
  1. $20^\circ$
  2. $30^\circ$
  3. $40^\circ$
  4. $45^\circ$
  5. $50^\circ$