## janessia 3 years ago Find the perimeter of the triangle at the right. Assume that the line segments are tangent to the circle.

1. janessia

2. janessia

@jim_thompson5910

3. janessia

@MathLegend

4. jim_thompson5910

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

5. janessia

mmmhhhmmm

6. jim_thompson5910

you'll see that 2 triangles form

7. janessia

yes

8. jim_thompson5910

namely, the smaller triangles inside the larger ones

9. jim_thompson5910

highlighted here|dw:1353204485777:dw|

10. janessia

ohk

11. jim_thompson5910

so if we know this |dw:1353204546161:dw|

12. jim_thompson5910

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

13. janessia

ohk yes i see that

14. janessia

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

15. jim_thompson5910

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

16. janessia

ohk

17. jim_thompson5910

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

18. jim_thompson5910

|dw:1353204871377:dw|

19. jim_thompson5910

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

20. jim_thompson5910

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

21. jim_thompson5910

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

22. jim_thompson5910

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

23. janessia

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

24. jim_thompson5910

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

25. jim_thompson5910

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

26. janessia

i get it so 58 is the answer

27. jim_thompson5910

yep