19 Draw a segment [AC] with AC = 15 cm.
Place the points 0 and F on this segment such that AO =
OF = 3 cm
On the perpendicular at O to (AC), place a point B such
that OB = 6 cm.
1° Prove that AB = 3V5 cm and that BC = 6V5 cm.
2° Prove that (AB) and (BC) are perpendicular.
3° Draw the circle (T) of diameter [CF] that cuts (BC)
again in H.
Prove that (AB) and (FH) are parallel.
4° Calculate CF then CH.
5° Prove that the triangle BAF is isosceles.
6º Draw from A the parallel to the line (BF).
It cuts the line (HF) at G.
Prove that ABFG is a rhombus and specify its perimeter.
7° Prove that the triangle OBC has the same area as the
rhombus AREG