Pleaaaase help me! What is the radius (r) of a circle inscribed in a "12-16-20" right triangle? The answer must be either a whole number, in reduced fraction form, or simplified radical form (no decimals). I can't paste the picture here but what it basically looks like is a right triangle with the two legs being 16 and 12 and the hypotenuse being 20. Inside the triangle is a circle and there is one radius line drwan in it...

Question

amistre64 · Answer

if you connect the angles with the midpoint of the opposite sides, you find the center of the triangle.... that much I have so far :)

anonymous · Answer

What do you know about incentres/incircles? I guess nothing, as then this would be trivial :/

amistre64 · Answer

I come to  radius=4.

If we take the intersection of the lines as the center for our circle, then y = 4... if I did it right :)

anonymous · Answer

You are right..

In general, the radius is (xy)/(x+y+z) - where z = hypotenuse.

amistre64 · Answer

y = (3/8)x

and

y = -(3/4)x + 12  is what I used

amistre64 · Answer

yay!!... im glad I was right :)  thanx

anonymous · Answer

I like your method, by the way. I've seen others answer questions like that with lines rather than geometric rules, and it always surprises me - I never spot to do things like that :(

amistre64 · Answer

x = 32/3  which when plugged in gets me y = 4 :)