Jean Monnet HS worksheet Prob EN rectangle

In rectangle ABCD, the sides are [math]BC=6[/math]cm and [math]CD=6\sqrt{3}[/math] cm, and the diagonals intersect at point O,[math]AC\cap BD=\left\{O\right\}[/math]. Knowing that E is the symmetric of point C with respect to B, and [math]OE\cap AB=\left\{F\right\}[/math], then:[br][*][b]1.[/b] Find the length of segment AE.[br][/*][*][b]2.[/b] Show that the perimeter of triangle BEF is less than 17 cm.[br][/*]

1.

Find the length of segment AE.

2. 1

Prove that F is the center of gravity in triangle AEC.

2.2

Find FB.

[math]4\sqrt{2}[/math] 8 [math]2\sqrt{3}[/math] [math]4\sqrt{3}[/math]

2.3

Find EF.

[math]3\sqrt{3}[/math] [math]\sqrt{3}[/math] [math]2\sqrt{3}[/math] [math]4\sqrt{3}[/math]

2.4

Perimeter of BEF triangle is:

[math]6+6\sqrt{3}[/math] [math]6+4\sqrt{3}[/math] [math]6+2\sqrt{3}[/math] 14.71

2.5

Prove: [math]P_{BEF}<17[/math]

Information: Jean Monnet HS worksheet Prob EN rectangle