Exercise 3 — Part A In a plane P, consider a triangle ABC right-angled at A. Let $d$ be the line orthogonal to plane P and passing through point B. Consider a point D on this line distinct from point B. 1. Show that the line (AC) is orthogonal to the plane (BAD). A bicoin is called a tetrahedron whose four faces are right triangles. 2. Show that the tetrahedron ABCD is a bicoin. 3. a. Justify that the edge $[CD]$ is the longest edge of the bicoin ABCD. b. Let I be the midpoint of edge $[CD]$. Show that point I is equidistant from the 4 vertices of the bicoin ABCD.
Exercise 3 — Part A
In a plane P, consider a triangle ABC right-angled at A. Let $d$ be the line orthogonal to plane P and passing through point B. Consider a point D on this line distinct from point B.
1. Show that the line (AC) is orthogonal to the plane (BAD).
A bicoin is called a tetrahedron whose four faces are right triangles.
2. Show that the tetrahedron ABCD is a bicoin.
3. a. Justify that the edge $[CD]$ is the longest edge of the bicoin ABCD.
b. Let I be the midpoint of edge $[CD]$. Show that point I is equidistant from the 4 vertices of the bicoin ABCD.