If CM = 8, DM = 6, and AB = 16, and if AM is longer than DM, find AM.

http://media01.switchedononline.com/a_matgeo_2010/6/group171.gif

Question

If CM = 8, DM = 6, and AB = 16, and if AM is longer than	 DM, find AM.

http://media01.switchedononline.com/a_matgeo_2010/6/group171.gif

anonymous · Answer

attachment

amistre64 · Answer

when we cross chords; the halfs multiply and equal ..

amistre64 · Answer

cm*md = am*mb

anonymous · Answer

So right now I have 
AM * MB = 8 * 6
AM + MB = 48
Where would I go from here?

amistre64 · Answer

am = x; mb = 16-x in this case

amistre64 · Answer

8*6 = x(16-x)

48 = 16x -x^2

x^2 -16x +48 = 0

anonymous · Answer

x² - 16x + 48 = 0

So how would I work this down?

Sorry I am not "geometrically inclined :D"

amistre64 · Answer

x^2 -16x+(64-64) +48 = 0

(x^2 -16x+64)+(-64 +48) = 0

(x-8)^2 - 16 = 0

(x-8)^2 = 16; when x = +-4 +8 = 4 and 12

amistre64 · Answer

we add a useful form of 0 that completes the square

anonymous · Answer

the answer is 0 ?

amistre64 · Answer

since am > dm

4 or 12 > 6; am = 12

anonymous · Answer

Oh my goodness! Thank you so much :D

It was right!

amistre64 · Answer

8 + 4 = 12

8-4 = 4; those are our options for am and mb

anonymous · Answer

The answer was 12 :)

Now only if I can apply all this to the other problems lol

amistre64 · Answer

:)  takes practice, but you can do it ..

anonymous · Answer

Thank you :D