tag:blogger.com,1999:blog-6933544261975483399.post1490395024218683809..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Routh's Theorem 3: Triangle, Cevians, Ratio, AreasAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6933544261975483399.post-27051399341187478142010-07-07T23:23:01.751-07:002010-07-07T23:23:01.751-07:00S1=Area(A’BC’) = ½ *BC’*BA’*sin(B) =1/2 *n*f*d*sin...S1=Area(A’BC’) = ½ *BC’*BA’*sin(B) =1/2 *n*f*d*sin(B)<br />S=Area(ABC)=1/2*AB*BC*sin(B)=1/2*(1+n)*f*(1+k)*d*sin(B)<br /> So S1/S=n/[(n+1)*(k+1)]<br />Calculate the same way for other ratios<br /><br />Peter TranPeter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-10557715514088240732010-03-23T13:19:23.062-07:002010-03-23T13:19:23.062-07:00SABA'/S = 1/1+k ( see P1) (1)
draw from B h1...SABA'/S = 1/1+k ( see P1) (1)<br />draw from B h1 altitude on C'A', and h2 from A on C'A'<br />=>h1/h2 = n<br />SAA'C' = C'A'∙h2 = C'A'∙h1/n<br />SBC'A' = C'A'∙h1<br />=><br />SAA'C'/SBC'A' = 1/n<br />=><br />SABA'/SBC'A' = (1+n)/n<br />=><br />(1/(1+k))/SBC'A' = (1+n)/n ( SABA' = 1/1+k from (1)<br /><br /><br />SBC'A' = n/(1+k)(1+n)<br />-----------------------------------------c .t . e. onoreply@blogger.com