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October 1st, 2011, 09:17 PM  #1 
Newbie Joined: Oct 2011 Posts: 10 Thanks: 0  General Area and Perimeter Calculation
Let ABC be an acuteangled triangle in which D, E, F are points on BC, CA, AB respectively, such that AD is perpendicular to BC, AE=EC and CF bisects angle C. Suppose CF meets AD and DE in M and N respectively. If FM=2, MN=1, NC=3, find the perimeter and area of triangle. I am having some difficulties in solving this problem. Can you guys help me??? 
October 2nd, 2011, 02:38 AM  #2 
Newbie Joined: Oct 2011 Posts: 10 Thanks: 0  Re: General Area and Perimeter CAlculation
Pls help me on this problem people..

October 3rd, 2011, 07:58 AM  #3 
Member Joined: Oct 2011 Posts: 81 Thanks: 0  Re: General Area and Perimeter Calculation
I've got many things here but i cannot reach on area part...:O

December 24th, 2017, 03:41 AM  #4 
Newbie Joined: Dec 2017 From: India Posts: 1 Thanks: 0  Let ABC be a acute angled triangle in which D,E,F are points on BC,CA,AB respectively
Given FN = NC = 3. In triangle ACF , CE/AE = CN /NF = 1. So, by midpoint theorem, EN  AF. => DE  AB. and EN = AF/2 In triangle ABC, CE = EA and DE  AB. So, by intercept theorem BD= DC. => ABC is an isosceles triangle with AB = AC. Consider triangles DMN and AMF. They are similar to each other by AA similarity criterion. So, DN/AF = MN/MF = ½. Therefore DN = EN = AF/2. In triangle CED, by angle bisector theorem CE/CD = EN/DN. But EN = DN. Therefore CE = CD => AC= BC. So, ABC is an equilateral triangle with altitude CF = 6. So, perimeter = 3 * AB = 3 * 2* CF/ sqrt(3). = 6* 6/ sqrt (3) = 12* sqrt(3)= 20.76 
December 24th, 2017, 05:44 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,608 Thanks: 845 
Nice solve OMC. Would have been easier if problem was stated: Find perimeter of equilateral triangle with height = 6 By the way, 12*sqrt(3) = ~20.78 Since Xmas tomorrow, you're forgiven NOTE: problem posted over 6 years ago... 

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