Problems(2)
Seven cookies of radius 1 inch are cut from a circle of cookie dough, as shown. Neighboring cookies are tangent, and all except the center cookie are tangent to the edge of the dough. The leftover scrap is reshaped to form another cookie of the same thickness. What is the radius in inches of the scrap cookie?[asy]
draw(circle((0,0),3));
draw(circle((0,0),1));
draw(circle((1,sqrt(3)),1));
draw(circle((-1,sqrt(3)),1));
draw(circle((-1,-sqrt(3)),1)); draw(circle((1,-sqrt(3)),1));
draw(circle((2,0),1)); draw(circle((-2,0),1)); [/asy]<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>1.5<spanclass=′latex−bold′>(C)</span>π<spanclass=′latex−bold′>(D)</span>2π<spanclass=′latex−bold′>(E)</span>π AMCAMC 10
All the numbers 1,2,3,4,5,6,7,8,9 are written in a 3×3 array of squares, one number in each square, in such a way that if two numbers are consecutive then they occupy squares that share an edge. The numbers in the four corners add up to 18. What is the number in the center?<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> 9 AMC10AMCAMC 10AMC 10 B