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2006 JHMT
8
8
Part of
2006 JHMT
Problems
(1)
2006 JHMT Geometry #8
Source:
9/1/2023
Circles
P
P
P
,
Q
Q
Q
, and
R
R
R
are externally tangent to one another. The external tangent of
P
P
P
and
Q
Q
Q
that does not intersect
R
R
R
intersects
P
P
P
and
Q
Q
Q
at
P
Q
P_Q
P
Q
and
Q
P
Q_P
Q
P
, respectively.
Q
R
Q_R
Q
R
,
R
Q
R_Q
R
Q
,
R
P
R_P
R
P
, and
P
R
P_R
P
R
are defined similarly. If the radius of
Q
Q
Q
is
4
4
4
and
Q
P
P
Q
‾
∥
R
Q
Q
R
‾
\overline{Q_PP_Q} \parallel \overline{R_QQ_R}
Q
P
P
Q
∥
R
Q
Q
R
, compute
R
P
P
R
R_PP_R
R
P
P
R
.
geometry