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Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
1993 Mexico National Olympiad
5
5
Part of
1993 Mexico National Olympiad
Problems
(1)
collinearity of intersections of diameters of 3 chords
Source: Mexican Mathematical Olympiad 1993 OMM P5
7/29/2018
O
A
,
O
B
,
O
C
OA, OB, OC
O
A
,
OB
,
OC
are three chords of a circle. The circles with diameters
O
A
,
O
B
OA, OB
O
A
,
OB
meet again at
Z
Z
Z
, the circles with diameters
O
B
,
O
C
OB, OC
OB
,
OC
meet again at
X
X
X
, and the circles with diameters
O
C
,
O
A
OC, OA
OC
,
O
A
meet again at
Y
Y
Y
. Show that
X
,
Y
,
Z
X, Y, Z
X
,
Y
,
Z
are collinear.
geometry
collinear
Chords