Author 
Topic 

Jack
Junior Member
USA
3 Posts 
Posted  05/09/2011 : 14:35:42

Can anybody HELP me with this problem? What is the length of diameter of a circle inscribed into a right triangle with the length of hypotenuse c and the sum of the lenghts of legs m. 


Jack
Junior Member
USA
3 Posts 
Posted  05/09/2011 : 16:07:42

I solved this problem by using Theorem that bisectors of angles of right triangle intersect in a center of inscribed circle. So diameter of this circle D equal : D=mc 


Subhotosh Khan
Advanced Member
USA
9117 Posts 
Posted  05/09/2011 : 17:01:43

quote: Originally posted by Jack
Can anybody HELP me with this problem? What is the length of diameter of a circle inscribed into a right triangle with the length of hypotenuse c and the sum of the lenghts of legs m.
Good work  Jack. 


TchrWill
Advanced Member
USA
80 Posts 
Posted  05/13/2011 : 14:13:15

What is the length of diameter of a circle inscribed into a right triangle with the length of hypotenuse c and the sum of the lenghts of legs m.
Incircle The internal circle tangent to the three sides and the incenter as center.
The radius of the inscribed circle is r = A/s where A = the area of the triangle and s = the semiperimeter = (a + b + c)/2, a, b, and c being the three sides.
The radius of the inscribed circle may also be derived from r = ab/(a + b + c).
The radius of the inscribed circle may also be derived from the particular m and n used in deriving a Pythagoraen Triple triangle by r = n(m  n).
If x, y, and z are the points of contact of the incircle with the sides of the triangl e A, B, C, then Cx = Cy = s  c, Bx = Bz = s  b, and Ay = Az = s  a.
The radius of an inscribed circle within a right triangle is equal to r = A/s = s  c where s = (a+b+c)/2 and c = the hypotenuse.

Edited by  TchrWill on 05/14/2011 11:46:20 



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