tag:blogger.com,1999:blog-6933544261975483399.post4851779261053780449..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1035: Triangle, Three equal Incircles, Tangent lines, Equivalent triangles, Equal areaAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-24729632279682495312014-08-15T14:17:44.788-07:002014-08-15T14:17:44.788-07:00You have a nice and simple solution.
Peter Tran
You have a nice and simple solution.<br />Peter Tran<br />Peter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-69553449863304502492014-08-15T01:24:19.400-07:002014-08-15T01:24:19.400-07:00Let s be the semi-perimeter of the two triangles o...Let s be the semi-perimeter of the two triangles of equal perimeter and r is the radius of the three circles congruent. <br />S1 is the area of triangle A1B1C1 and S2 the area of triangle A2B2C2. <br />In addition, S is the area of the hexagon A1B2C1A2B1C2 and A (A1B2C1) is the area of the triangle A1B2C1. <br />S = S1 + A (A1B2C1) + A (C1A2B1) + A (B1C2A1) = S1 + r s <br />S = S2 + A (C2A1B2) + A (B2C1A2) + A (A2B1C2) = S2 + r s <br />From the comparison it follows: S1 = S2.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-18208746934858306132014-07-31T06:07:52.321-07:002014-07-31T06:07:52.321-07:00To Dima
Problem 1035
Please, Carry out your plan a...To Dima<br />Problem 1035<br />Please, Carry out your plan applying Heron and check each step<br />Can you see clearly that the step is correct?<br />ThanksAntonio Gutierrezhttps://www.blogger.com/profile/04521650748152459860noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-62658378930475351222014-07-31T00:20:51.961-07:002014-07-31T00:20:51.961-07:00As we had proved in problem 1034, the perimeters a...As we had proved in problem 1034, the perimeters are equal so by applying Heron's theorem <br />in both of the triangles,it will give the same result.Anonymoushttps://www.blogger.com/profile/02970933367484538195noreply@blogger.com