tag:blogger.com,1999:blog-6933544261975483399.post2950669822269567527..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1175: Six Tangential or Circumscribed Quadrilaterals Antonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-26303832016926586102016-01-10T10:54:58.714-08:002016-01-10T10:54:58.714-08:00I get your point Peter.
In a quadrilateral if th...I get your point Peter. <br /><br />In a quadrilateral if the diagonals bisect the angles the quadrilateral is easily shown to be tangential with the point of intersection of the diagonals the centre of this in circle <br /><br />The converse is not necessarily true <br /><br />If for example U is the centre of circle within BNKJ, V of KLGF and W of GHDR,then<br /><br />UKV and VGW are collinear but BUK and GWD need not necessarily be so. <br /><br />Hence my proof is fallacious <br /><br />Thanks Peter<br /><br />Antonio /Peter - any ideas as to how my proof could be corrected? Sumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-85723651145067477612016-01-09T19:44:37.357-08:002016-01-09T19:44:37.357-08:00To Sumith Peiris
Refer to your solution
1. In gen...To Sumith Peiris<br /><br />Refer to your solution<br />1. In general case diagonal BK of tangential quadrilateral BNKJ is not bisect angle B or angle D . Please justify for statement.<br />2. In my opinion B, K, G, D are not collinear as per your solution. Please justify<br /><br />Peter Tran<br />Peter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-65053747183179336042016-01-07T22:55:26.603-08:002016-01-07T22:55:26.603-08:00BK must bisect angles < B and < K. KG simila...<br />BK must bisect angles < B and < K. KG similarly < K and < G and GD < G and D. Hence BKGD is collinear and bisects < B and < D<br /><br />Similarly AFLC can be shown to be collinear bisecting < A and < C<br /><br />So the diagonals of ABCD AC and BD bisect the 4 angles and hence ABCD must be a tangential quadrilateral <br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-9770090938680497792016-01-07T19:26:29.448-08:002016-01-07T19:26:29.448-08:00This problem is almost identical to problem 883.
s...This problem is almost identical to problem 883.<br />see link below for the solution.<br /><br />http://gogeometry.blogspot.com/2013/06/problem-883-five-tangential-or.html<br /><br />Peter TranPeter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.com