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# Mathematics Brain Teasers. ## Recommended Posts  On 10/1/2020 at 6:55 PM, Ozymandias said:

Since nobody is bothering to upload another teaser and I have one of my own to hand ..............

Problem: a triangle ABC has sides 7m, 8m and 9m in length. Its area is 26.833m^2. What is the radius of its incircle?

I'll give the answer to this problem tomorrow as nobody seems interested and. like the last time, we can let this thread die a death.

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#### Posted Images  On 10/3/2020 at 12:12 PM, Ozymandias said:

I'll give the answer to this problem tomorrow as nobody seems interested and. like the last time, we can let this thread die a death.

Problem: a triangle ABC has sides 7m, 8m and 9m in length. Its area is 26.833m^2. What is the radius of its incircle?

Solution: The area of the triangle ABC is 26.833m^2 and is made up of the area of the triangle ABO, ACO and BCO. Each of these three triangles have a base equal to one of the sides of ABC and a perpendicular height, r, equal to the radius of the incircle.

Area ABC      =  area ABO + area ACO + area BCO

26.833m^2    =  1/2(8)(r) + 1/2(9)(r) + 1/2(7)(r)

26.833m^2    =  1/2(r)(8 + 9 + 7)

r    =   26.833/[1/2(24)]       =       2.236m to the nearest millimetre

Edited by Ozymandias
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