janessia
Find the perimeter of the triangle at the right. Assume that the line segments are tangent to the circle.



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janessia
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janessia
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@jim_thompson5910

janessia
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@MathLegend

jim_thompson5910
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if you cut the figure up like this
dw:1353204276912:dw

janessia
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mmmhhhmmm

jim_thompson5910
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you'll see that 2 triangles form

janessia
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yes

jim_thompson5910
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namely, the smaller triangles inside the larger ones

jim_thompson5910
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highlighted heredw:1353204485777:dw

janessia
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ohk

jim_thompson5910
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so if we know this
dw:1353204546161:dw

jim_thompson5910
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then we can say this as well
dw:1353204577254:dw

janessia
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ohk yes i see that

janessia
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so then can we say that the other side is 9 as well?

jim_thompson5910
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let me think, I'm looking for justification that the two larger triangles are congruent

janessia
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ohk

jim_thompson5910
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oh wait, not sure why i didn't see this til now lol

jim_thompson5910
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dw:1353204871377:dw

jim_thompson5910
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the smaller two triangles in the lower right corner are isosceles triangles

jim_thompson5910
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you have to draw another line to see this if you can't

jim_thompson5910
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so that's why we can add the extra 9 on there
the 6 comes from the fact that 9+6 = 15

jim_thompson5910
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so to finish things off, we get this full picture
dw:1353204976827:dw

janessia
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ohk why did u choose 9 and 6... those arent the only things that add together to get 15

jim_thompson5910
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yes, but the 9 is locked in, which is why the second segment has to be a 6

jim_thompson5910
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if you don't see what I mean, go back to a previous drawing where I show how the second 9 (the lower 9) shows up

janessia
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i get it so 58 is the answer
