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 December 26th, 2012, 01:06 PM #1 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 find area of BDC 1) could someone find out the are of triangle BDC: given that A is the circumcenter point of BDC E is the incenter point of BAC and |EI| = 0.72 F is the incenter point of BAD and |FH| = 1 G is the incenter point of DAC and |GJ| = 0.6 NOTE: the angles D,B,C are smaller then 90� 2) find area of EFG ---------------------------------------------------------- answers: 1) 14.83 2) 1.1 December 27th, 2012, 09:13 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: find area of BDC Sure wish you'd have triangle BCD on x-axis, with D at origin! Haven't done the solving yet (not sure if I will!) but here's one with all-integers: areaBCD = 290304 BD = 624 BC = 960 CD = 1008 AB = AC = AD = 520 FH = 156 (AF = 260) EI = 96 (AE = 104) GJ = 63 (AG = 65) In case you wanted to "play" with an integer case  December 27th, 2012, 10:58 AM #3 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 Re: find area of BDC you really love integers don't you  December 29th, 2012, 12:39 PM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: find area of BDC Code: C M B A OK Jelly, using mine to "do the work"; problem statement: M is the circumcenter of acute triangle ABC, so AM = BM = CM. The inradius of triangle ABM = 63 The inradius of triangle ACM = 96 The inradius of triangle BCM = 156 Calculate sides of triangle ABC (same as yours, right?) I think this'll work: Apply rs = Area = sqrt(s(s-a)(s-b)(s-c)) to triangles ABM, ACM, BCM. Let AM = BM = CM = R. AB = 2 R sin(C) , BC = 2 R sin(A), AC = 2 R sin(B) R sin(C)cos(C) / (1 + sin(C)) = 63 R sin(B)cos(B) / (1 + sin (B)) = 96 R sin(A)cos(A) / (1 + sin(A)) = 156 A + B + C = pi. 4 equations, 4 unknowns: should be ok, right? Try it... December 30th, 2012, 08:12 AM   #5
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Re: find area of BDC

Quote:
 Originally Posted by Denis R sin(C)cos(C) / (1 + sin(C)) = 63 R sin(B)cos(B) / (1 + sin (B)) = 96 R sin(A)cos(A) / (1 + sin(A)) = 156
i don't see how you get to those and i don't see how can be proven
but i'll ask that in a separate post December 30th, 2012, 09:51 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: find area of BDC R sin(C)cos(C) / (1 + sin(C)) = 63 R sin(B)cos(B) / (1 + sin (B)) = 96 R sin(A)cos(A) / (1 + sin(A)) = 156 .................................................. .......................................... Angles are: A = 36.869897.... , B = 67.380135.... , C = 75.749967.... And R = 520. 520 * sin(75.749967) * cos(75.749967) / [1 + sin(75.749967)] = 63 520 * sin(67.380135) * cos(67.380135) / [1 + sin(67.380135)] = 96 520 * sin(36.869897) * cos(36.869897) / [1 + sin(36.869897)] = 156 December 31st, 2012, 07:36 AM #7 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 Re: find area of BDC yes but just how you found those 3 equations, how you got to them? December 31st, 2012, 09:13 AM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: find area of BDC Forgot exactly where/how, but I use them as a "fait accompli"! I think you'll see why here: http://mathworld.wolfram.com/Inradius.html Bonne et heureuse annee  January 2nd, 2013, 03:28 AM   #9
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Re: find area of BDC

[attachment=0:2n7qvt2p]Area of BCD.jpg[/attachment:2n7qvt2p]
the calculation is too tedious
hope gelatine1 can post your solution
Attached Images Area of BCD.jpg (63.3 KB, 195 views) January 2nd, 2013, 08:55 AM   #10
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Re: find area of BDC

Quote:
 Originally Posted by Denis Bonne et heureuse annee merci et je vous souhaitez aussi une bonne ann�e Quote:
 Originally Posted by albert.teng hope gelatine1 can post your solution
i have no solution i just randomly made a question and found the answer with some program. just because it's an intresting problem and i am learning quite alot from this Tags area, bdc, find Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post johnny993 Algebra 1 November 12th, 2013 09:17 PM Albert.Teng Algebra 2 July 21st, 2012 12:17 AM Arley Calculus 3 April 28th, 2012 09:22 AM seit Calculus 4 November 14th, 2010 05:48 AM 450081592 Calculus 7 January 19th, 2010 02:45 AM

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