tag:blogger.com,1999:blog-6933544261975483399.post6784535563447054793..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Problem 268: Right Triangle, Catheti and AltitudeAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-53468530276037630752020-12-09T13:55:46.570-08:002020-12-09T13:55:46.570-08:00See the drawing
Define c=AB
S=[ABC]=a.b/2=c.h/2 =...See the <a href="http://sciences.heptic.fr/2020/12/08/gogeometry-problem-268/" rel="nofollow"><b>drawing</b></a><br /><br />Define c=AB<br />S=[ABC]=a.b/2=c.h/2 => a.b=c.h<br />c=a.b/h => c^2=a^2.b^2/h^2<br />Pythagoras => a^2+b^2=c^2<br />=> a^2+b^2=a^2.b^2/h^2<br />dividing by a^2.b^2 => <b>1/b^2 + 1/a^2 = 1/h^2</b>rv.littlemanhttps://www.blogger.com/profile/05572092955468280791noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-44383103084935726252020-03-25T04:13:19.981-07:002020-03-25T04:13:19.981-07:00https://www.youtube.com/watch?v=Pxuw-ro45ZAhttps://www.youtube.com/watch?v=Pxuw-ro45ZAGeek37https://www.blogger.com/profile/12171388277139538068noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-80659519389543778182009-08-31T10:06:34.569-07:002009-08-31T10:06:34.569-07:00By JCA
1/a^2+1/b^2=(a^2+b^2)/(a^2*b^2)=c^2/(a^2*b^...By JCA<br />1/a^2+1/b^2=(a^2+b^2)/(a^2*b^2)=c^2/(a^2*b^2)<br />=1/h^2*(c^2*h^2)/(a^2*b^2)<br />=1/h^2*(4[ABC]^2)/(4*[ABC]^2]=1/h^2Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-87083081008135204582009-05-21T00:19:03.527-07:002009-05-21T00:19:03.527-07:00We know that a^2 = BH*BA, b^2 = AH*BA and h^2=AH*B...We know that a^2 = BH*BA, b^2 = AH*BA and h^2=AH*BH. So 1/a^2 + /b^2 = 1/BH*BA + 1/AH*BA = 1/BA*[1/BH+1/AH] = 1/c * [AH+BH=c)/AH*BH = 1/(AH-BH) = 1/h^2. Hence, 1/a^2 + /b^2 = 1/h^2<br />Ajit: ajitathle@gmail.comAjithttps://www.blogger.com/profile/00611759721780927573noreply@blogger.com