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マイナー構図bot @Geometry_Arc

メモです Joined September 2024
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Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

5 months ago

三角形ABCと弧BC上の点Pについて，半直線BP,CP上にそれぞれ点E,FをAP=PE=PFを満たすようにとる．このとき，Pに依らず直線EFは常にある定点(= A-傍心)を通る．

Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

6 months ago

三角形ABCについて，その内心をI，外心をOとする．直線AIが円ABCと再び交わる点をVとし，OIの中点をSとしたとき，AIの垂直二等分線，OVの垂直二等分線及びSを通りVSに垂直な直線は一点で交わる．

Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

6 months ago

三角形ABCとPについて，Pを通る直線が直線BC,CA,AB及び円PBC,PCA,PABと交わる点をそれぞれD,E,F,X,Y,Zとする．このとき，7円ABC,AEZ,AFY,BFX,BDZ,CDY,CEXは共点である．

Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

6 months ago

三角形ABCについて，BCの中点をMとし，弧BC(Aを含まない)の中点をVとする．四角形ANMVが等脚台形となるように点Nを取ったとき，ANを直径とする円は円ABC, B-傍接円, C-傍接円に接する．

Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

6 months ago

投稿して欲しいジャンルやマイナー度の要望があればぜひ教えてください。

Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

8 months ago

三角形ABCについて，その外心をOとし，任意の点Pの垂足三角形をΔとする．このとき，Δの面積はPOの長さにのみ依存する．(Simsonの定理の拡張)

Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

8 months ago

2円ω1,ω2 (ω1<ω2)が2点A,Bで交わっており，さらに共通外接線はTで交わっている．このとき，∠ATBはω1におけるABの円周角とω2におけるABの円周角の差に等しい．

Geometry_Arc Profile Picture

マイナー構図bot @Geometry_Arc

8 months ago

三角形ABCと点K,L,Pについて，K,Lのチェバ三角形をそれぞれA_0B_0C_0,DEFとし，直線PA_0,PB_0,PC_0が円PBC,PCA,PABと再び交わる点をそれぞれA_1,B_1,C_1とする．直線A_1D,B_1E,C_1Fが円PBC,PCA,PABと再び交わる点をそれぞれX,Y,Zとしたとき，4点P,X,Y,Zは共円．

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