MathDB

10

Part of 2008 AMC 10

Problems(2)

Bisecting Square Sides

Source: AMC 10 2008A Problem 10

2/22/2008
Each of the sides of a square S1 S_1 with area 16 16 is bisected, and a smaller square S2 S_2 is constructed using the bisection points as vertices. The same process is carried out on S2 S_2 to construct an even smaller square S3 S_3. What is the area of S3 S_3? <spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 4 <span class='latex-bold'>(A)</span>\ \frac {1}{2} \qquad <span class='latex-bold'>(B)</span>\ 1 \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ 3 \qquad <span class='latex-bold'>(E)</span>\ 4
geometryAMC
Arc Segment

Source: AMC 12 2008B Problem 9

2/29/2008
Points A A and B B are on a circle of radius 5 5 and AB\equal{}6. Point C C is the midpoint of the minor arc AB AB. What is the length of the line segment AC AC? <spanclass=′latex−bold′>(A)</span> 10<spanclass=′latex−bold′>(B)</span> 72<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 15<spanclass=′latex−bold′>(E)</span> 4 <span class='latex-bold'>(A)</span>\ \sqrt{10} \qquad <span class='latex-bold'>(B)</span>\ \frac{7}{2} \qquad <span class='latex-bold'>(C)</span>\ \sqrt{14} \qquad <span class='latex-bold'>(D)</span>\ \sqrt{15} \qquad <span class='latex-bold'>(E)</span>\ 4
trigonometrygeometrypower of a pointPythagorean TheoremAMC