Circle A and circle B are congruent. CD is a chord of both circles If CD = 16 cm and the radius is 17 cm, how long is AB?

Question

anonymous · Answer

superdavesuper · Answer

Note that AB n CD bi-sect each other....let's call the point where they cross each other X....so AX=XB and CX=?

anonymous · Answer

DX?

superdavesuper · Answer

yup good job! as CD is given, u know CX=DX=?

anonymous · Answer

Got lost sorry CD=16  ...CX=DX= lost sorry

superdavesuper · Answer

look at the pic....CD=___ + ___ right?

anonymous · Answer

CD=16 +__ not sure what the next blank is

superdavesuper · Answer

Since we call the intersection point X, now the line CD is divided into two parts; CX and DX right? And u just said CX=DX....

anonymous · Answer

So I divided 16?

superdavesuper · Answer

yes divided it by 2 n u get CX

anonymous · Answer

8
?

superdavesuper · Answer

hahaha why the ? com'on u KNOW 16/2=8 :P

anonymous · Answer

Lol just making sure I'm correct lol

superdavesuper · Answer

OK now look at the triangle AXC....notice <X is a right-angle....

anonymous · Answer

Yes I see that

anonymous · Answer

Yes I see that?

superdavesuper · Answer

So u know this property about right-angle triangle: a^2 + b^2 = c^2? where c is the longest side?

anonymous · Answer

Yes Pythagorean Therom  familiar with it

superdavesuper · Answer

Cool so applying it for triangle AXC then....

anonymous · Answer

so am I doing 8^2 * 8^2 =c^2

superdavesuper · Answer

Nope...just write it out in terms of AX^2, CX^2 and AC^2 first plz?

anonymous · Answer

Okay I wrote down on my work out paper  AX^2 * CX^2 AC^2

superdavesuper · Answer

U already know CX=8 and AC=raidus so look it up from ur Question...

anonymous · Answer

Cx=8 Ac=17

superdavesuper · Answer

so put them into ur eqn u get....

anonymous · Answer

18.7

superdavesuper · Answer

Nope set up ur eqn first plz?

anonymous · Answer

8^2 +17^2=

superdavesuper · Answer

Which side of the = sign AC^2 should be on? Left or right?

anonymous · Answer

Left?

superdavesuper · Answer

read Pythagorean Therom: AC is the longest side...

anonymous · Answer

Ohhh ... Right then !

superdavesuper · Answer

Right on :) soooooo.....

anonymous · Answer

Have to work backwards ......8^2+ ___=17^2

superdavesuper · Answer

yup yup

anonymous · Answer

15?

superdavesuper · Answer

that is the right answer :)

anonymous · Answer

thankyou ! so much

superdavesuper · Answer

welcome n thanks 4 working w me hehee