tag:blogger.com,1999:blog-6933544261975483399.post7522142514255681394..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1120: Isosceles Right Triangle, 120 Degree, Angle, Equilateral, Metric RelationsAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-8456844244792827292018-06-27T03:18:14.499-07:002018-06-27T03:18:14.499-07:00Sketch is not openSketch is not openKAMAL SINGHhttps://www.blogger.com/profile/15566453526398693769noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-63345308916833746812015-09-11T01:55:10.620-07:002015-09-11T01:55:10.620-07:00See the sketchSee the sketchPeter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-86732708164043765362015-07-28T02:05:39.485-07:002015-07-28T02:05:39.485-07:00Where point G is determineWhere point G is determinesmithmathhttps://www.blogger.com/profile/09779796531613955165noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-72896031216346740412015-06-13T10:31:25.529-07:002015-06-13T10:31:25.529-07:00http://s1.postimg.org/d51e4r4cf/pro_1120.png
Let ...http://s1.postimg.org/d51e4r4cf/pro_1120.png<br /><br />Let O is circumcentre of triangle BEC<br />Let AB=BC= m and AC= m. √ (2)<br />Let ∠ (BCE)= θ<br />Triangle EDF have 2 60 degrees angles so EDF is equilateral <br />1. We have OGC is 30-60-90 triangle so OC= m/√(3)<br />And e=EC= 2.m/sqrt(3). cos(θ +30) with chord= m and angle of position= θ<br />Similarly with circumcircle of triangle ABF with chord=m and angle of position= θ+30 we have <br />F=BE= 2.m/√ (3). cos(θ +60)<br />Similarly with circumcircle of triangle ADC with chord= m. sqrt(2) and angle of position= θ +15 we have<br />d=AD= 2.m/√ (3). Sqrt(2).cos(θ +45)<br /><br />2. e+f= 2.m/√ (3) . [ cos(θ +30)+ cos(θ +60)]<br />Replace cos(θ +30)+ cos(θ +60) = 2. Cos(θ +45). Cos(15)<br />So d/(e+f)= 1/(√ (2). Cos(15))<br />Replace cos(15)= (√(6)+ √(2))/4 and simplify we get<br />d/(e+f)= √ (3)-1<br />Peter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.com