Radius of incircle of a triangle = Area of triangle/Semiperimeter of the triangle. How?

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Radius of incircle of a triangle = Area of triangle/Semiperimeter of the triangle. How?

Mathematics
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Who said that?
  • phi
|dw:1327066868311:dw|
You meant the sum?

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Other answers:

no....my textbook just says that formula. we're supposed to apply that formula in approrpriate sums. im asking for the formula's proof :P
says* = states
  • phi
The center of the incircle is the intersection of the angle bisectors You end up with 6 right triangles for example, 2 with sides a and r add up the area of each
???
  • phi
Not clear yet?
kind of.....not fully
  • phi
|dw:1327067491979:dw|
oh. wait. stop right there. :P I got it :D Thanks a lot :)
  • phi
|dw:1327067560181:dw|
  • phi
These 2 triangles are congruent. Angle bisector makes angles =, 90 deg =, 3rd angle must be equal, plus they have equal side (radius)
I understood, phi. I intitally had problems with how you derived it, and then now i got it. Thanks.
Got it as in I got the answer. :)
  • phi
It's nice when the light bulb goes on!
lol yup, totally :D!

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