CONSIDER A CIRCLE S. THE POINT P LIES OUTSIDE S AND A LINE IS DRAWN...

3. - ĐỀ THI OLYMPIC TOÁN HỌC QUỐC TẾ BMO NĂM 2012
Toán ĐỀ THI OLYMPIC TOÁN HỌC QUỐC TẾ BMO NĂM 2012

3. Consider a circle S. The point P lies outside S and a line is drawn

• One complete solution will gain more credit than

through P , cutting S at distinct points X and Y . Circles S

1

and S

2

several unfinished attempts. It is more important

are drawn through P which are tangent to S at X and Y respectively.

to complete a small number of questions than to

Prove that the difference of the radii of S

1

and S

2

is independent of

try all the problems.

the positions of P, X and Y .

• Each question carries 10 marks. However, earlier

questions tend to be easier. In general you are