Difference between revisions of "2003 AMC 12B Problems"
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== Problem 22 == | == Problem 22 == | ||
− | == Problem == | + | == Problem 22== |
Let <math>ABCD</math> be a [[rhombus]] with <math>AC = 16</math> and <math>BD = 30</math>. Let <math>N</math> be a point on <math>\overline{AB}</math>, and let <math>P</math> and <math>Q</math> be the feet of the perpendiculars from <math>N</math> to <math>\overline{AC}</math> and <math>\overline{BD}</math>, respectively. Which of the following is closest to the minimum possible value of <math>PQ</math>? | Let <math>ABCD</math> be a [[rhombus]] with <math>AC = 16</math> and <math>BD = 30</math>. Let <math>N</math> be a point on <math>\overline{AB}</math>, and let <math>P</math> and <math>Q</math> be the feet of the perpendiculars from <math>N</math> to <math>\overline{AC}</math> and <math>\overline{BD}</math>, respectively. Which of the following is closest to the minimum possible value of <math>PQ</math>? | ||
Revision as of 19:02, 1 February 2010
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 22
- 24 Problem 23
- 25 Problem 24
- 26 Problem 25
- 27 See also
Problem 1
Which of the following is the same as
?
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Let be a 5-digit number, and let q and r be the quotient and remainder, respectively, when
is divided by 100. For how many values of
is
divisible by 11?
Problem 19
Let be the set of permutations of the sequence
for which the first term is not
. A permutation is chosen randomly from
. The probability that the second term is
, in lowest terms, is
. What is
?
Problem 20
Problem 21
An object moves cm in a straight line from
to
, turns at an angle
, measured in radians and chosen at random from the interval
, and moves
cm in a straight line to
. What is the probability that
?
Problem 22
Problem 22
Let be a rhombus with
and
. Let
be a point on
, and let
and
be the feet of the perpendiculars from
to
and
, respectively. Which of the following is closest to the minimum possible value of
?
![[asy] size(200); defaultpen(0.6); pair O = (15*15/17,8*15/17), C = (17,0), D = (0,0), P = (25.6,19.2), Q = (25.6, 18.5); pair A = 2*O-C, B = 2*O-D; pair P = (A+O)/2, Q=(B+O)/2, N=(A+B)/2; draw(A--B--C--D--cycle); draw(A--O--B--O--C--O--D); draw(P--N--Q); label("\(A\)",A,WNW); label("\(B\)",B,ESE); label("\(C\)",C,ESE); label("\(D\)",D,SW); label("\(P\)",P,SSW); label("\(Q\)",Q,SSE); label("\(N\)",N,NNE); [/asy]](http://latex.artofproblemsolving.com/c/2/2/c22d4d20155faaf8bd0cf51f26a5795d14b32322.png)