MathDB

Nepal National Olympiad

Source: Nepal Mathematics Olympiad

April 22, 2018

geometry

Problem Statement

Problem Section #3
a) Circles

O_1

and

O_2

interest at two points

B

and

C

, and

BC

is the diameter of circle

O_1

. Construct a tangent line of circle

O_1

at

C

and intersecting circle

O_2

at another point

A

. Join

AB

to intersect circle

O_1

at point

E

, then join

CE

and extend it to intersect circle

O_2

at point

F

. Assume

H

is an arbitrary point on line segment

D

. Join

HE

and extend it to intersect circle

O_1

at point

G

, and then join

BG

and extend it to intersect the extend of

AC

at point

D

. Prove:

\frac{AH}{HF}=\frac{AC}{CD}

.

Back to Problems View on AoPS