J'ai un cadeau pour toi 
A semicircular arc ° is drawn on AB as diameter. C is a point on ° other
than A and B; and D is the foot of the perpendicular from C to AB: We
consider three circles, °1; °2; °3, all tangent to the line AB: Of these, °1 is
inscribed in ¢ABC; while °2 and °3 are both tangent to CD and to °, one on
each side of CD: Prove that °1; °2 and °3 have a second tangent in common.