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# geometry questions

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1.  The perimeter of a triangle is 12 and its inradius is 1. What is the area of the triangle? 2.  is the incenter of Triangle ABC. We have CE=12, AE=9, and AB=12. Find BC. Nov 11, 2019

#1
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Why would you put both these question on one post?

That makes no sense to me.

Nov 11, 2019
edited by Melody  Nov 11, 2019
#2
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1. We can assume that the triangle is equilateral, so the area is sqrt(3)/4*(12/2)^2 = 9 sqrt(3).

2. From similar triangles, BC = (12 + 12)/(12 + 9)*12 = 96/7.

Nov 11, 2019
#3
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The inradius  is the height of three smaller triangles with the sum of their bases = the perimeter of the large triangle

So.....the area of the large triangle is

(1/2) (perimeter) ( 1)  =

(1/2) (12) * 1  =

6 units^2   Nov 11, 2019
#4
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Second one

The incenter  is the point where the angle  bisectors meet

Therefore  BE  is an angle bisector.....so we have the relationship that

AB / AE  =  BC  / EC

12 / 9  =  BC  / 12    cross-multiply

12 * 12  =  BC * 9

12 * 12 / 9  = BC

144 / 9  =  BC   =   16   Nov 11, 2019