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.

Since BD = DC and BC = 12, BD = 6. Since BC = 12 and MC = 11, BM = 1. Thus, MD = 5. AMD is a right triangle with a hypotenuse of 10, and MD = 5, so AM = sqrt(10^2 - 5^2) = 5 sqrt(3). AMC is also a right triangle with legs 5 sqrt(3) and 11. AC, the hypotenuse, is sqrt(75 + 121) = 14.

Posted by friedlinguini on 2002-07-01 06:21:07