ช่วยทีครับ
Given $4$ points in plane. If the areas of four triangles formed are different positive integer. and $6$ distances between those $4$ points are also $6$ different positive integers, then the convex closure of $4$ points is called a "lotus design"
$(1)$ Construct an example of "lotus design". Also what are areas and distances in your example $?$
$(2)$ Prove that there are infinitely many "lotus design" which are not similar.
|