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The center, O, of the inscribed circle is at the intersection of the angle bisectors AD and CO, which is at the same distance from the sides of the triangle.
DO = EO is the radius of the circle.
We can use the given measures of the triangle sides and a little trigonometry to find radius DO
Angles DCO and ECO are congruent and their measure is half the measure of angle BCA.
Using the trigonometric identity for half angles
we can calculate
and from there we can find radius DO.