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Let $ABC$ be an equilateral triangle.

$D$ is on $BC$ and $\angle BAD = 20^\circ$.

Also let $I_1$, $I_2$ be the inner centers of triangles $ABD$, $ACD$ respectively.

$E$ is a point making the triangle $I_1I_2E$ be equilateral ($D$ and $E$ are on the opposite side of the line $I_1I_2$.

Then what is the $\angle ADE$?

This is my question and I tried to find $4$ cyclic points or something like that, but I have no idea.

Please help me.

scarface
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EUNSUNG LIM
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  • You should add a diagram of this: what has the point $;E;$ to do with triangle $;I_1I_2B;$ ?? Also, from what I could gather, this triangle $;I_1I_2B;$ is going to have a non-acute angle always ....Very unclear. – DonAntonio Apr 05 '17 at 22:13
  • Sorry i edited.. – EUNSUNG LIM Apr 06 '17 at 02:59

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