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 Circle inscribed into right triangle

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T O P I C    R E V I E W
Jack 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.
3   L A T E S T    R E P L I E S    (Newest First)
TchrWill 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 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.




Subhotosh Khan 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.
Jack 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=m-c

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