3

Problems(2)

Determining a point on plane with ratio of distances minimal

Source: Vietnam MO 1981 P3

3/17/2011

A plane

\rho

and two points

M, N

outside it are given. Determine the point

A

\rho

for which

\frac{AM}{AN}

is minimal.

ratiogeometry unsolvedgeometry

older geometry

Source:

6/22/2006

Two circles

k_1

and

k_2

with centers

O_1

and

O_2

respectively touch externally at

A

. Let

M

be a point inside

k_2

and outside the line

O_1O_2

. Find a line

d

through

M

which intersects

k_1

and

k_2

again at

B

and

C

respectively so that the circumcircle of

\Delta ABC

is tangent to

O_1O_2

geometrycircumcircleperpendicular bisectorgeometry proposed