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MathNet 2019-part-05 — 184 problems (EN–VI) Question 100

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 100

A triangle $ABC$ has $AB = AC$ and $\angle BAC = 110^\circ$. A point $D$ is taken on the perpendicular bisector of the segment $[AC]$, inside triangle $ABC$, so that $\angle DAC = 25^\circ$, and a point $E$ is taken on $BC$, so that $BE = AD$.

a) Find the measure of $\angle AED$.

b) Prove that $D$ is the circumcenter of the triangle $AEC$.