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# Triangle Bisectors

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What is the radius of the circle inscribed in triangle ABC if AB = 10, AC = 17, BC = 21? Express your answer as a decimal to the nearest tenth.

Oct 7, 2018

#1
+101234
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We can find the area of this triangle using Heron's Formula

s  = [ 10 + 17 + 21  ] / 2  =  48 / 2  = 24

The area  =  √ [ s (s - 10) (s - 17) (s - 21) ]  =

√ [ 24 (14) (7) (3) ] =

√7056   = 84  units^2

The area   =  1/2  [ sum of triangle's sides ]  *  altitude of each triangle

But....the altitude of each triangle  = the radius  of the incircle

So...we have

84  = (1/2) (48) * radius of incircle

84  = 24 * radius of incircle

84 / 24  = rasius of incircle  = 3.5 units

EDIT TO CORRECT AN ERROR  !!!!

Oct 7, 2018
edited by CPhill  Oct 8, 2018
#2
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CPhill: There is a minor typo in Heron's formula calculation:
sqrt(24 (24 - 21) (24 - 17) (24 - 10))
Sqrt[24 x 3 x 7 x 14]
Sqrt[7,056] =84 - the area of the triangle.

Oct 7, 2018
#3
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Thank you guest and CPhill

Oct 8, 2018