Difference between revisions of "2006 AMC 12B Problems/Problem 23"
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== Problem == | == Problem == | ||
| − | {{ | + | Isosceles <math>\triangle ABC</math> has a right angle at <math>C</math>. Point <math>P</math> is inside <math>\triangle ABC</math>, such that <math>PA=11</math>, <math>PB=7</math>, and <math>PC=6</math>. Legs <math>\overline{AC}</math> and <math>\overline{BC}</math> have length <math>s=\sqrt{a+b\sqrt{2}{</math>, where <math>a</math> and <math>b</math> are positive integers. What is <math>a+</math>b<math>? |
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| + | </math>\mathrm{(A)}\ 85\qquad\mathrm{(B)}\ 91 \qquad\mathrm{(C)}\ 108\qquad\mathrm{(D)}\ 121\qquad\mathrm{(E)}\ 127$ | ||
== Solution == | == Solution == | ||
Revision as of 20:49, 16 April 2009
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Problem
Isosceles 
has a right angle at 
. Point 
is inside , such that 
, 
, and 
. Legs 
and 
have length $s=\sqrt{a+b\sqrt{2}{$ (Error compiling LaTeX. Unknown error_msg), where 
and 
are positive integers. What is 
b
\mathrm{(A)}\ 85\qquad\mathrm{(B)}\ 91 \qquad\mathrm{(C)}\ 108\qquad\mathrm{(D)}\ 121\qquad\mathrm{(E)}\ 127$
Solution
See also
| 2006 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 22 |
Followed by Problem 24 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
