MathDB

22

Part of 2003 AMC 10

Problems(2)

Rectangle and Lines

Source:

1/2/2009
In rectangle ABCD ABCD, we have AB\equal{}8, BC\equal{}9, H H is on BC \overline{BC} with BH\equal{}6, E E is on AD \overline{AD} with DE\equal{}4, line EC EC intersects line AH AH at G G, and F F is on line AD AD with GFAF \overline{GF}\perp\overline{AF}. Find the length GF GF. [asy]unitsize(3mm); defaultpen(linewidth(.8pt)+fontsize(8pt));
pair D=(0,0), Ep=(4,0), A=(9,0), B=(9,8), H=(3,8), C=(0,8), G=(-6,20), F=(-6,0);
draw(D--A--B--C--D--F--G--Ep); draw(A--G); label("FF",F,W); label("GG",G,W); label("CC",C,WSW); label("HH",H,NNE); label("66",(6,8),N); label("BB",B,NE); label("AA",A,SW); label("EE",Ep,S); label("44",(2,0),S); label("DD",D,S);[/asy]<spanclass=latexbold>(A)</span> 16<spanclass=latexbold>(B)</span> 20<spanclass=latexbold>(C)</span> 24<spanclass=latexbold>(D)</span> 28<spanclass=latexbold>(E)</span> 30 <span class='latex-bold'>(A)</span>\ 16 \qquad <span class='latex-bold'>(B)</span>\ 20 \qquad <span class='latex-bold'>(C)</span>\ 24 \qquad <span class='latex-bold'>(D)</span>\ 28 \qquad <span class='latex-bold'>(E)</span>\ 30
geometryrectangle
Clock's Chimes

Source:

1/9/2009
A clock chimes once at 30 30 minutes past each hour and chimes on the hour according to the hour. For example, at 1 PM there is one chime and at noon and midnight there are twelve chimes. Starting at 11:15 AM on February 26 26, 2003 2003, on what date will the 2003rd 2003^{\text{rd}} chime occur? <spanclass=latexbold>(A)</span> March 8<spanclass=latexbold>(B)</span> March 9<spanclass=latexbold>(C)</span> March 10<spanclass=latexbold>(D)</span> March 20<spanclass=latexbold>(E)</span> March 21 <span class='latex-bold'>(A)</span>\ \text{March 8} \qquad <span class='latex-bold'>(B)</span>\ \text{March 9} \qquad <span class='latex-bold'>(C)</span>\ \text{March 10} \qquad <span class='latex-bold'>(D)</span>\ \text{March 20} \qquad <span class='latex-bold'>(E)</span>\ \text{March 21}