# IMO 1999 Bucharest geometry problem

Submitted by Structure on Thu, 01/08/2009 - 21:15.Two circles and are contained inside the circle G, and are tangent to G at the

distinct points M and N, respectively. passes through the center of . The line

passing through the two points of intersection of and meets G at A and B.

The lines MA and MB meet at C and D, respectively.

Prove that CD is tangent to

[geo]

(point O 186 193)

(point R 85 308)

(circle t O R)

(pointoncircle M t 134 49)

(pointoncircle N t 305 290)

(segment MO M O)

(segment NO N O)

(pointonline O1 MO 175 163)

(circle t1 O1 M)

# Power of a point with respect to a circle

Submitted by Structure on Sat, 11/29/2008 - 18:29.Two lines by a point P outside a circle cut in A,B respectively in C and D. Then

as