MathDB

11

Part of 2012 AMC 10

Problems(2)

Externally Tangent Circles

Source: 2012 AMC10A Problem #11

2/8/2012
Externally tangent circles with centers at points AA and BB have radii of lengths 55 and 33, respectively. A line externally tangent to both circles intersects ray ABAB at point CC. What is BCBC?
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 4.8<spanclass=′latex−bold′>(C)</span> 10.2<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 14.4 <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 4.8 \qquad<span class='latex-bold'>(C)</span>\ 10.2 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ 14.4
analytic geometrygraphing linesslopeAMC
Dessert Chef and Yummy Desserts

Source: 2012 AMC10B Problem #11

2/23/2012
A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?
<spanclass=′latex−bold′>(A)</span> 729<spanclass=′latex−bold′>(B)</span> 972<spanclass=′latex−bold′>(C)</span> 1024<spanclass=′latex−bold′>(D)</span> 2187<spanclass=′latex−bold′>(E)</span> 2304 <span class='latex-bold'>(A)</span>\ 729\qquad<span class='latex-bold'>(B)</span>\ 972\qquad<span class='latex-bold'>(C)</span>\ 1024\qquad<span class='latex-bold'>(D)</span>\ 2187\qquad<span class='latex-bold'>(E)</span>\ 2304
symmetryrotationAMC