The Unknown Side (Posted on 2002-07-01)

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.

	Submitted by Dulanjana
Rating: 2.9091 (11 votes)
Solution:	(Hide)
DB = CB / 2 = 12 / 2 = 6 MB = CB - CM = 12 - 11 = 1 DM = DB - MB = 6 - 1 = 5 DM^2 + AM ^2 = AD^2 (pythagorean), so 25 + AM^2 = 100 AM = sqrt(75) CA^2 = AM^2 + CM^2 (pythagorean), so CA = sqrt(75 + 121) = sqrt(196) = 14

	Subject	Author	Date
	re(2): Puzzle Resolution	K Sengupta	2022-03-24 20:42:23
	re: Puzzle Resolution	Ady TZIDON	2012-07-17 10:04:32
	Puzzle Resolution	K Sengupta	2007-06-15 12:21:11
	answer	K Sengupta	2007-06-15 12:17:16
	re: Trouble with the solution	Jim	2005-10-14 20:38:26
	Trouble with the solution	B	2004-12-03 17:10:04
	Solution	Antonio	2003-09-04 07:28:26
	Pythagoras would like this	mark hartman	2003-05-30 12:32:56
	solution	rob allen	2003-02-04 09:09:59
	Pythagoras	Michael	2003-02-02 23:33:45
	re(2): Why Angle A?	TomM	2002-07-01 10:03:34
	re: Why Angle A?	levik	2002-07-01 09:37:18
	2 + 2 = 5 Doh!	TomM	2002-07-01 08:49:31
	Why Angle A?	TomM	2002-07-01 08:41:18
	Solution	friedlinguini	2002-07-01 06:21:07
	try..	Cheradenine	2002-07-01 05:10:22