С In the figure below we have the 2 circles (CD) and (c) of the same center O and their radii are
R = 2cm and R2 = 4cm respectively. A straight line passing through O cuts (C) at F and A
and cuts (C) at B and E. The tangent to circle
(C:) at A cuts the circle (C) at C and D.
01) Show that (CD) is the perpendicular
bisector of [OB].
2) Determine the nature of the triangle OBC.
3) Show that the quadrilateral OCBD is a
thombus.
4) Let P be the midpoint of [CE].
a. Calculate OP and deduce that P belongs
to the circle (C1).
b. Show that D, O and P are collinear.
c. Show that (OP) is perpendicular to (CE)
and deduce that (CE) is tangent to (C1).
d. Show that (CO) is perpendicular to
(DE).
A
BU
0
D​