ABC is a triangle:

Angle A < 90.

D is a point on BC such that BD = DC.

M is a point on BC such that AM is perpendicular to BC.

If

AD = 10,

BC = 12 and

MC = 11
find the length of AC.

AC is 14.
Just takes two applications of the Pythagorean Theorem:

DC is 6 so DM is 5 and triangle MDA is a right triangle, so by the Pythagorean Theorem, MA is Square root of 75. But triangle MCA is also a right triangle, so by Pythagoras, AC^2 = 75 + 11^2. AC^2 = 196, so AC = 14.

Posted by mark hartman on 2003-05-30 12:32:56