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What is the radius of the circle inscribed in triangle ABC if AB = 22, AC=12, BC=14? Express your answer in simplest radical form.

shreyas1  Oct 4, 2018
 #1
avatar+92376 
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We can find the area of this triangle using Heron's Formula

 

s  =  [ 22 + 12 + 14 ] / 2  = 48/2  =  24

 

The area is given by :

 

√[ 24 (24 - 22) (24 - 12) (24 - 14)  = √ [24 * 2 * 12 * 10 ]  = √[48 * 120] = 24√10

 

Because the radius of the inscribed circle is perpendicular to each side of the triangle...three triangles are formed.......each with a height = to the circle's radius and with bases of 22, 12 and 14 respectively

 

So...the area of the triangle can be expressed as

 

Area  = (1/2)r [ 22 + 12 + 14]     where r is the altitude of each triangle = the radius of the inscribed circle

 

Solving for r we have

 

r  =   2* Area / [ 22 + 12 + 14 ]   =

 

2 * 24√10 / [ 48]  = 

 

48√10 / 48 =

 

√10  units

 

 

cool cool cool

CPhill  Oct 4, 2018
edited by CPhill  Oct 4, 2018

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