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The problem of inscribed circle of right triangle
1、? O passing through the center of the circle is a three-sided vertical line. According to the definition, O is the intersection of bisectors of triangle angles, so the lengths of three vertical lines are equal, which is equal to the radius r? s△ABC = 1/2AC * BC = 1/2(AC+BC+AB)* r? ①

Where BC = 5 and AB = √( AC & amp; sup2+BC & amp; Sup2) into equation (1).

Get AC= 12 and AB= 13? △ABC =5+ 12+ 13=30 perimeter.

2、? As an auxiliary line, as in the first question,1/2bc =1/2 (a+b+c) * r.

R=bc/(a+b+c)