Math CentralQuandaries & Queries


Question from Angie, a student:

Circle O is inscribed in triangle ABC. Angle A = 50 and angle B = 60. Find arc XY in degrees

Hi Angie,

You didn't tell us what $X$ and $Y$ are. I assume they are as in my diagram where $D$ is the center of the circle and you are to find the measure of the angle $XDY.$


If I am correct then I suggest that you use two facts.

  1. Angles $CXD$ and $DYC$ are right angles.

  2. The center of an inscribed circle in a triangle lies on the angle bisectors.


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