Geometry Stumper

[Albert Chan]

(08-14-2018 08:35 PM)Thomas Puettmann Wrote:  A standard theorem from elementary geometry says that all three (interior) angular bisectors meet at one point, namely, the center of the inscribed circle.

I "see" the solution !

The twist in this puzzle is the "inscribed" circle is on the outside.
But the circle still "inscribed" the lines, if you extend the lines.

If you extend line BC, and you are at B, there is 3 angles left of C
Angle(ACB) + 2 * Angle(ACD) = 180 degree (since it is just line extension)

using symmetry, the other side have the same constraint:
Angle(ACB) + 2 * Angle(BCE) = 180 degree

Add the two equations, then divide by 2:
Angle(ACD) + Angle(ACB) + Angle(BCE) = 180 degree

--> Angle(DCE) = 180 degree

Thanks.