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 Geometry and Trigonometry
 Circle inscribed into right triangle
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Jack
Junior Member

USA
3 Posts

Posted - 05/09/2011 :  14:35:42  Show Profile  Reply with Quote
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.
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Jack
Junior Member

USA
3 Posts

Posted - 05/09/2011 :  16:07:42  Show Profile  Reply with Quote
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=m-c
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 05/09/2011 :  17:01:43  Show Profile  Reply with Quote
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.
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TchrWill
Advanced Member

USA
80 Posts

Posted - 05/13/2011 :  14:13:15  Show Profile  Reply with Quote
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 semi-perimeter = (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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