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SMO 2013 Open Round 1 Question 13

SMO · SMO 2013 Open Round 1

Question 13

In the triangle $ABC$, a circle passes through the point $A$, the midpoint $E$ of $AC$, the midpoint $F$ of $AB$ and is tangent to the side $BC$ at $D$. Suppose

$$\frac{AB}{AC}+\frac{AC}{AB}=4.$$

Determine the size of $\angle EDF$ in degrees.