MathDB

16

Part of 2010 AMC 10

Problems(2)

Find the minimum perimeter of the triangle

Source:

2/10/2010
Nondegenerate △ABC \triangle ABC has integer side lengths, BD BD is an angle bisector, AD \equal{} 3, and DC \equal{} 8. What is the smallest possible value of the perimeter? <spanclass=′latex−bold′>(A)</span> 30<spanclass=′latex−bold′>(B)</span> 33<spanclass=′latex−bold′>(C)</span> 35<spanclass=′latex−bold′>(D)</span> 36<spanclass=′latex−bold′>(E)</span> 37 <span class='latex-bold'>(A)</span>\ 30 \qquad <span class='latex-bold'>(B)</span>\ 33 \qquad <span class='latex-bold'>(C)</span>\ 35 \qquad <span class='latex-bold'>(D)</span>\ 36 \qquad <span class='latex-bold'>(E)</span>\ 37
geometryperimeterAMC 10 2010 number 16
A Square and a Circle

Source: 2010 AMC 10B Problem 16

2/25/2010
A square of side length 1 1 and a circle of radius 3/3 \sqrt3/3 share the same center. What is the area inside the circle, but outside the square? (A)\ \frac{\pi}3 \minus{} 1 \qquad(B)\ \frac{2\pi}{9} \minus{} \frac{\sqrt3}3 \qquad(C)\ \frac{\pi}{18} \qquad(D)\ \frac14 \qquad(E)\ 2\pi/9
geometrysymmetryPythagorean TheoremAMC