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Chile Contests
Chile National Olympiad
1996 Chile National Olympiad
6
6
Part of
1996 Chile National Olympiad
Problems
(1)
equal arcs wanted, 2 intersecting circles (1996 Chile NMO P6)
Source:
11/22/2021
Two circles,
C
C
C
and
K
K
K
, are secant at
A
A
A
and
B
B
B
. Let
P
P
P
be a point on the arc
A
B
AB
A
B
of
C
C
C
. Lines
P
A
PA
P
A
and
P
B
PB
PB
intersect
K
K
K
again at
R
R
R
and
S
S
S
respectively. Let
P
′
P'
P
′
be another point at same arc as
P
P
P
, so that lines
P
′
A
P'A
P
′
A
and
P
′
B
P'B
P
′
B
again intersect
K
K
K
at
R
′
R'
R
′
and
S
′
S'
S
′
, respectively. Prove that the arcs
R
S
RS
RS
and
R
′
S
′
R'S'
R
′
S
′
have equal measures. https://cdn.artofproblemsolving.com/attachments/2/4/88693c36159179fb2b098b671a2f8281b37aae.png
geometry
arcs
arc