a) Cho (IKsubset left( SAK right)), tìm (left( SAK right)cap left( SBD right)).
+ S là điểm chung thứ nhất.
+ Trong (left( ABCD right)) gọi (E=AKcap BDRightarrow left{ begin{align} Ein AKsubset left( SAK right)Rightarrow Ein left( SAK right) Ein BDsubset left( SBD right)Rightarrow Ein left( SBD right) end{align} right.Rightarrow Ein left( SAK right)cap left( SBD right)).
(Rightarrow E) là điểm chung thứ hai.
(Rightarrow left( SAK right)cap left( SBD right)=SE).
Trong (left( SAK right)) gọi (M=IKcap SE) ta có (left{ begin{align} Min IK Min SEsubset left( SBD right) end{align} right.Rightarrow M=IKcap left( SBD right)).
b) Cho (SDsubset left( SBD right)), tìm (left( SBD right)cap left( IJK right)).
+ (left{ begin{align} Min IKsubset left( IJK right)Rightarrow Min left( IJK right) Min SEsubset left( SBD right)Rightarrow Min left( SBD right) end{align} right.Rightarrow Min left( SBD right)cap left( IJK right)Rightarrow M) là điểm chung thứ nhất.
+ Trong (left( ABCD right)) gọi (F=IKcap BD) ta có: (left{ begin{align} Fin IKsubset left( IJK right)Rightarrow Fin left( IJK right) Fin BDsubset left( SBD right)Rightarrow Fin left( SBD right) end{align} right.Rightarrow Fin left( SBD right)cap left( IJK right)Rightarrow F) là điểm chung thứ hai.
(Rightarrow left( SBD right)cap left( IJK right)=MF).
Trong (left( SBD right)) gọi (N=MFcap SD) ta có:
(left{ begin{align} Nin SD Nin MFsubset left( IJK right)Rightarrow Nin left( IJK right) end{align} right.Rightarrow N=SDcap left( IJK right)).
* Tìm (SCcap left( IJK right)).
Cho (SCsubset left( SCD right)), tìm (left( CD right)cap left( IJK right)).
Trong (left( ABCD right)) gọi (G=JKcap CD) ta có: (left{ begin{align} Gin JKsubset left( IJK right)in Gin left( IJK right) Gin CDsubset left( SCD right)Rightarrow Gin left( SCD right) end{align} right.Rightarrow Gin left( IJK right)cap left( SCD right)).
(Rightarrow G) là điểm chung thứ nhất.
+ N là điểm chung thứ hai.
(Rightarrow left( SCD right)cap left( IJK right)=GN).
Trong (left( SCD right)) gọi (H=SCcap GNRightarrow H=SCcap left( IJK right)).
