Question

A medal to whoever solves it:

http://gyazo.com/921394ac5ec0296703faae05b20a2e37

Answer 1

AD=AE

Answer 2

AE=13 so thats your answer :)

Answer 3

Ah, ok . Thank you. I have a bit more after thus one, if you'd like me to tag you in them for medals.

Answer 4

sure

Answer 5

Cool, gonna go ahead and close this one.

Answer 6

okay

Answer 7

@Chop-GTA5 how do you know that AD = AE (just curious)

Answer 8

cause AE is the same length as AD

Answer 9

thats what im asking, how do you know that?

Answer 10

do you have a justification, or you just used a ruler and measured it?

Answer 11

wait i think it might be 11.1 now :/

Answer 12

Hrm, 11.1?

Answer 13

well we know that triangle ADC is similar to triangle AEB

Answer 14

therefore AC/AB = AD/AE

Answer 15

So it is 13?

Answer 16

plugging in we have
6/7 = AD / 13

AD = 13 * 6/7 = 11.1

Answer 17

Ohh, alright. Thank you Perl :).

Answer 18

do you see why the two triangles are similar ?

Answer 19

i shouldn't say 'we know that', rather 'it can be shown'

Answer 20

Yeah.

Answer 21

<BDC intercepts the same arc as <CEB

Answer 22

therefore those two angles are the same. and note also that triangles ADC and AEB share that angle A at the corner.

Whats cool about geometry is that you can solve this without a ruler. Of course you can get out a ruler and find the length manually. But with geometry you can find the exact answer, (a ruler only gives you approximation), and it involved no tools :)

Answer 23

that is the power of geometry , using pure reasoning you can get solutions that involves no approximating