tag:blogger.com,1999:blog-6933544261975483399.post2797812481633558485..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1214: Triangle, Three Angle Bisectors, ProportionsAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-16993077215041528482016-05-24T07:46:42.189-07:002016-05-24T07:46:42.189-07:00c((a - f)/f) = a((c - e)/e)
((a - f)/f)/a = ((c - ...c((a - f)/f) = a((c - e)/e)<br />((a - f)/f)/a = ((c - e)/e)/c<br />1/f - 1/a = 1/e - 1/c<br />1/a + 1/e = 1/c + 1/fAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-79910414447010082902016-05-18T12:30:20.620-07:002016-05-18T12:30:20.620-07:001) c/AD=a/DC => 1.1)AD/DC=c/a
2) (c-e)/AD=e/B...1) c/AD=a/DC => 1.1)AD/DC=c/a <br />2) (c-e)/AD=e/BD<br />3)(a-f)/DC=f/BD<br />from 2) & 3) 1.2) AD/DC=(c-e)f/(a-f)e<br />from 1.1 &1.2 it's provedc.t.e.onoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-24743593912224867942016-05-18T09:05:46.565-07:002016-05-18T09:05:46.565-07:00Let AD = y; AC = x AND BD = z.
Applying angle Bis...Let AD = y; AC = x AND BD = z. <br />Applying angle Bisector to triangle ABC => x/y = a/c --------- (1)<br />Applying angle Bisector to triangle ABD => y/z = (c-e)/e ----------- (2)<br />Applying angle Bisector to triangle BDC => x/z = (a-f)/f -----------(3)<br /><br />(3)/(2) => x/y = a/c = e.(a-f)/f.(c-e)<br />=> af(c-e) = ce(a-f)<br />=> a(c/e-1) = c(a/f-1)<br />=> 1/e-1/f = (a-c)/ac<br />=> 1/a+1?e = 1/c+1/fSailendra Thttps://www.blogger.com/profile/12056621729673423024noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-73729326410690613972016-05-18T09:00:40.229-07:002016-05-18T09:00:40.229-07:00c/a
= AD/DC
= (AD/BD) / (DC/BD)
= ((c - e)/e) / ((...c/a<br />= AD/DC<br />= (AD/BD) / (DC/BD)<br />= ((c - e)/e) / ((a - f)/f)<br /><br />ace - cef = acf - aef<br />1/f - 1/a = 1/e - 1/c<br />1/a + 1/e = 1/c + 1/fJacob HA (EMK2000)https://www.blogger.com/profile/17238561555526381028noreply@blogger.com