Difference between revisions of "2018 AMC 12B Problems/Problem 13"
(Redirected page to 2018 AMC 10B Problems/Problem 15) |
|||
Line 1: | Line 1: | ||
− | + | ==Problem== | |
+ | |||
+ | Square <math>ABCD</math> has side length <math>30</math>. Point <math>P</math> lies inside the square so that <math>AP = 12</math> and <math>BP = 26</math>. The centroids of <math>\triangle{ABP}</math>, <math>\triangle{BCP}</math>, <math>\triangle{CDP}</math>, and <math>\triangle{DAP}</math> are the vertices of a convex quadrilateral. What is the area of that quadrilateral? | ||
+ | |||
+ | <asy> | ||
+ | unitsize(120); | ||
+ | pair B = (0, 0), A = (0, 1), D = (1, 1), C = (1, 0), P = (1/4, 2/3); | ||
+ | draw(A--B--C--D--cycle); | ||
+ | dot(P); | ||
+ | defaultpen(fontsize(10pt)); | ||
+ | draw(A--P--B); | ||
+ | draw(C--P--D); | ||
+ | label("$A$", A, W); | ||
+ | label("$B$", B, W); | ||
+ | label("$C$", C, E); | ||
+ | label("$D$", D, E); | ||
+ | label("$P$", P, N*1.5+E*0.5); | ||
+ | dot(A); | ||
+ | dot(B); | ||
+ | dot(C); | ||
+ | dot(D); | ||
+ | </asy> | ||
+ | |||
+ | |||
+ | <math>\textbf{(A) }100\sqrt{2}\qquad\textbf{(B) }100\sqrt{3}\qquad\textbf{(C) }200\qquad\textbf{(D) }200\sqrt{2}\qquad\textbf{(E) }200\sqrt{3}</math>[/quote] | ||
+ | |||
+ | ==Solution== |
Revision as of 18:50, 16 February 2018
Problem
Square has side length
. Point
lies inside the square so that
and
. The centroids of
,
,
, and
are the vertices of a convex quadrilateral. What is the area of that quadrilateral?
[/quote]