find the length of x in the circle.

Question

anonymous · Answer

attachment

anonymous · Answer

what formula would i set up to solve this?

anonymous · Answer

Ah I remember talking to ya @clynnew it's been awhile though. Anyways: This is going to be a pain to set up but by the looks and math of it, looks like your length is: 19. Formula however would be 3 x 3 x3 x 10 /h (+3)x-3 = 19. To be honest I'm pretty bad at this stuff. However this may be wrong, I'm pretty positive 19 is the length though. However length across the whole circle is 7.5

anonymous · Answer

i remember too :) okay and do you mean x or * ?

anonymous · Answer

like 3*3*3*10/h(+3)x-3=19 or are they suppoed to be x

anonymous · Answer

Sorry I was AFK, they are supposed to be X @clynnew

campbell_st · Answer

you need to join the centre of the circle to the endpoints of the chord that contains 3 and x to form 2 triangles... 

then you prove the triangles are congruent using some circle geometry facts

and then can find the length of x

anonymous · Answer

So is the equation @StudyShark2000 set up for me correct ?

anonymous · Answer

@campbell_st

anonymous · Answer

@clynnew I'm 80% sure I am correct on the equation! Like I said I'm not very good at this but at the same time I know a little of formula equations. But yes your equation is all set up for you :)

campbell_st · Answer

the value of x can't be found using an equation... 

you need to show that the 2 triangles are congruent...

anonymous · Answer

can you walk me through that then @campbell_st ?

campbell_st · Answer

ok|dw:1429733237197:dw|

campbell_st · Answer

so you need to state the theorem you used to prove the congruency and then make a statement about the correspoding sides

anonymous · Answer

well AAA would be the theorem, correct ?

anonymous · Answer

how do i find x doing that ?

campbell_st · Answer

no AAA needs 3 angles and isn't a proof for congruency...

anonymous · Answer

OH because they are congruent x=3 i just need to prove that they are congruent to show that, 

SAS because BC = CD and both have angle C

campbell_st · Answer

that's correct... the congruency is proven by SAS 

so the corresponding sides in congruent triangles are x and 3  so as you said, x = 3

job done

campbell_st · Answer

and don't forget AC is a common side....

anonymous · Answer

alright!! that makes sense, i definitely wasnt thinking to split it into two triangles.