Question 76
Amy has drawn three points in a plane, $A$, $B$, and $C$, such that $AB = BC = CA = 6$. Amy is allowed to draw a new point if it is the circumcenter of a triangle whose vertices she has already drawn. For example, she can draw the circumcenter $O$ of triangle $ABC$, and then afterwards she can draw the circumcenter of triangle $ABO$.
a) Prove that Amy can eventually draw a point whose distance from a previously drawn point is greater than $7$.
b) Prove that Amy can eventually draw a point whose distance from a previously drawn point is greater than $2019$.
(Recall that the circumcenter of a triangle is the center of the circle that passes through its three vertices.)
a) Prove that Amy can eventually draw a point whose distance from a previously drawn point is greater than $7$.
b) Prove that Amy can eventually draw a point whose distance from a previously drawn point is greater than $2019$.
(Recall that the circumcenter of a triangle is the center of the circle that passes through its three vertices.)