4
11. Triangle ABC has AB=13, BC=14, and AC=15. The points D, E, and
F are the mid-points of
, and
respectively. Let be
the intersection of the circumcircles of BDE and CEF. What is
XA+XB+XC?
(A)24 (B)
(C)
(D)
(E)
12. Let
be a triangle with sides 2011, 2012, and 2013. For , if
and D, E, and F are the points of tangency of the incircle
of to the sides AB, BC and AC, respectively, then
is a
triangle with side lengths AD, BE, and CF, if it exists. What is the
perimeter of the last triangle in the sequence
?
(A)
(B)
(C)
(D)
(E)
13. Square PQRS lies in the first quadrant. Points (3,0), (5,0), (7,0), and
(13,0) lie on lines SP, RQ, PQ, and SR, respectively. What is the sum
of the coordinates of the center of the square PQRS?
(A)6 (B)6.2 (C)6.4 (D)6.6 (E)6.8
14. In BAC, ∠BAC=40°, AB=10, and AC=6. Point D and E lie on
and
respectively. What is the minimum possible value of
BE+DE+CD?
(A)
(B)
(C)
(D)14 (E)
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