Question 1199419
Just a very small piece of help:
Notice the triangle is special 30-60-90 type.  Length <s>BA</s> AC is 10 cm.


Also, if you draw a segment from point B to the tangency point, you cut the triangle into two similar triangles.  You may remember or find a rule which gives some information about this.


If you use these and setup a proportion for the circle's radius, r, ....
you may find {{{cross(r=10/sqrt(5))}}}.  
<s>(Rationalize if you feel you want to.)</s>