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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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if you cut the figure up like this |dw:1353204276912:dw|
mmmhhhmmm
you'll see that 2 triangles form
yes
namely, the smaller triangles inside the larger ones
highlighted here|dw:1353204485777:dw|
ohk
so if we know this |dw:1353204546161:dw|
then we can say this as well |dw:1353204577254:dw|
ohk yes i see that
so then can we say that the other side is 9 as well?
let me think, I'm looking for justification that the two larger triangles are congruent
ohk
oh wait, not sure why i didn't see this til now lol
|dw:1353204871377:dw|
the smaller two triangles in the lower right corner are isosceles triangles
you have to draw another line to see this if you can't
so that's why we can add the extra 9 on there the 6 comes from the fact that 9+6 = 15
so to finish things off, we get this full picture |dw:1353204976827:dw|
ohk why did u choose 9 and 6... those arent the only things that add together to get 15
yes, but the 9 is locked in, which is why the second segment has to be a 6
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
i get it so 58 is the answer
yep

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