MathDB

3

Part of 1981 Vietnam National Olympiad

Problems(2)

Determining a point on plane with ratio of distances minimal

Source: Vietnam MO 1981 P3

3/17/2011
A plane ρ\rho and two points M,NM, N outside it are given. Determine the point AA on ρ\rho for which AMAN\frac{AM}{AN} is minimal.
ratiogeometry unsolvedgeometry
older geometry

Source:

6/22/2006
Two circles k1k_1 and k2k_2 with centers O1O_1 and O2O_2 respectively touch externally at AA. Let MM be a point inside k2k_2 and outside the line O1O2O_1O_2. Find a line dd through MM which intersects k1k_1 and k2k_2 again at BB and CC respectively so that the circumcircle of ΔABC\Delta ABC is tangent to O1O2O_1O_2.
geometrycircumcircleperpendicular bisectorgeometry proposed