tag:blogger.com,1999:blog-6933544261975483399.post7677922365848885288..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1298 Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, MidpointAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-24504792429505065722022-08-05T15:46:57.600-07:002022-08-05T15:46:57.600-07:00I do not see anybody have solution 0f 2nd part ...I do not see anybody have solution 0f 2nd part of the question " show that P is the midpoint of IH "Peter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-29933916880156823002016-12-25T09:07:48.338-08:002016-12-25T09:07:48.338-08:00Problem 1298
1. Let K medium the arc AB and ...Problem 1298<br />1. Let K medium the arc AB and L medium the arc BC.Is <BTC=<BTA=45 then the points B,P ant T are collinear.But <TAC+<TCA=90 or (45-<KAT)+(<ACT-45)=90 or <KAT=<ACT=<LTC=<KTA so <KTL=90. Is <KTO=<KTA+<ATO=<KAT+<TAO=45=<OTL.So <KTA=<ITP=<IPT=<BIH. But <BIH+<IBH=<KAT+45+<TAB=45+45=90. So IP is perpendicular in AC.<br /> APOSTOLIS MANOLOUDIS KORYDALLOS PIRAEUS GREECE<br /><br />APOSTOLIS MANOLOUDIShttps://www.blogger.com/profile/15561495997090211148noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-35603747292120490282016-12-24T18:08:56.040-08:002016-12-24T18:08:56.040-08:00https://goo.gl/photos/yYwMDZZwhsdpYQ2w9
Let D is ...https://goo.gl/photos/yYwMDZZwhsdpYQ2w9<br /><br />Let D is the midpoint of arc AC with ∠AOD= 90 ( see sketch)<br />Since TP is the angle bisector of angle ATC => TP will pass thru D<br />Since Triangles TIP and TOD are isoceless and angle ITP= angle OTD=> Angle TOD= angle TIP <br /> So IP//OD and IP ⊥AC<br />Peter Tranhttps://www.blogger.com/profile/02320555389429344028noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-23680967669616450502016-12-24T14:16:51.860-08:002016-12-24T14:16:51.860-08:00Draw TO. Ang HOI=2A, ang ITP=45-A => ang HIO = ...Draw TO. Ang HOI=2A, ang ITP=45-A => ang HIO = 90 - 2A<br />=> IHO = 90c.t.e.onoreply@blogger.com