help!

If AB = 12, CD = 12, and MD = 3, and if AM is the shorter segment, find AM

Question

help!

If AB = 12, CD = 12, and MD = 3, and if AM is the shorter segment, find AM

anonymous · Answer

attachment

anonymous · Answer

I remember some theorem ....AMxMB = CM x MD

anonymous · Answer

AM * MB = CM * 3
AM + MB = 12
CM + 3 = 12
CM = 9

anonymous · Answer

not sure though...... is m the center

anonymous · Answer

AM * MB = 27
AM = 27 / MB
MB + 27/MB = 12
MB ^2 + 27 = 12MB
MB = 9 
AM = 3

anonymous · Answer

just checked the theorem is true....also works for secants,and tangents
now we know CM = 9,DM = 3,AB = AM+MB and from the theorem AM = 27/MB
solve the last 2 equations getting a quadratic .Which will give you the answer.

anonymous · Answer

AM = 9

anonymous · Answer

AM is the shortest segment so = 3  (MB =3 or 9 are the roots of the quadratric but AM is the shortest segment so its 12 - 9 = 3)

anonymous · Answer

yes, you're right ...I missed that..I meant AM could also be 9....

anonymous · Answer

ok - happy with that cherri?