tag:blogger.com,1999:blog-6933544261975483399.post6045108618160359163..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Elearn Geometry Problem 222: Viviani Theorem, Exterior pointAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6933544261975483399.post-38657009566572692732018-01-17T11:16:22.713-08:002018-01-17T11:16:22.713-08:00Draw a line through the point D parallel to the li...Draw a line through the point D parallel to the line AC. Extend BF to meet the line parallel to AC in the point P. And also extend the line BE to meet the line parallel to AC in the point Q.<br /><br />Extend the line BH to meet the lin PQ in the point N. Then :<br /><br />BN=h+g <br /><br />Draw a altitude from the point P onto the line BQ. Because the triangle BPQ is equilateral.<br /><br />PM=BN=h+g<br /><br />From problem 223 we also know that :<br /><br />PM=e+f<br /><br />Therefore :<br /><br />e+f=h+g<br />e+f-g=h<br /><br />Arifhttps://www.blogger.com/profile/16774426807135540272noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-42329776232497001552009-04-14T20:51:00.000-07:002009-04-14T20:51:00.000-07:00Join D to A & C. Now Tr. ABC = Area DABC - Tr ...Join D to A & C. Now Tr. ABC = Area DABC - Tr ADC = Tr.DAB + Tr. DAC -Tr.ADC Hence, <br />Tr.ABC = Tr.DAB + Tr. DAC -Tr.ADC or<br />AC*h/2 = AB*f/2 + AC*e/2 - AC*g/2 or<br />h = f + e - g<br />QED<br />Ajit: ajitathle@gmail.comAjithttps://www.blogger.com/profile/00611759721780927573noreply@blogger.com