I am struggling with reconciling the fact that all the middle lines are the same length with the fact that the angles aren't the same.
2026-02-23 08:24:56.1771835096
GRE geometry questions about finding the angle between a side of a triangle and a circumradius
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Just try to draw the figure. Each of the triangles with peak at $D$ is isosceles, so the base angles are equal. That gives $\angle DBC=20^\circ$ so $\angle CDB=140^\circ$. $ADC$ is equilateral so $\angle CDA=60^\circ$. That leaves $\angle ADB=160^\circ$ Now just draw a circle, put a protractor at the middle, and draw the radii from the center at those angles. You will have the desired triangle.