2

Part of 1999 Turkey MO (2nd round)

Problems(1)

Turkey NMO 1999, P-2,a relation on a circle

Source:

Problem-2: Given a circle with center

O

, the two tangent lines from a point

S

outside the circle touch the circle at points

P

Q

SO

intersects the circle at

A

B

B

S

X

be an interior point of minor arc

PB

OS

intersect lines

QX

PX

C

D

, respectively. Prove that

\frac{1}{\left| AC \right|}+\frac{1}{\left| AD \right|}=\frac{2}{\left| AB \right|}

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