Difference between revisions of "2015 AMC 12B Problems/Problem 19"
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In <math>\triangle ABC</math>, <math>\angle C = 90^\circ</math> and <math>AB = 12</math>. Squares <math>ABXY</math> and <math>ACWZ</math> are constructed outside of the triangle. The points <math>X</math>, <math>Y</math>, <math>Z</math>, and <math>W</math> lie on a circle. What is the perimeter of the triangle? | In <math>\triangle ABC</math>, <math>\angle C = 90^\circ</math> and <math>AB = 12</math>. Squares <math>ABXY</math> and <math>ACWZ</math> are constructed outside of the triangle. The points <math>X</math>, <math>Y</math>, <math>Z</math>, and <math>W</math> lie on a circle. What is the perimeter of the triangle? | ||
| − | <math>\textbf{(A)}\; | + | <math>\textbf{(A)}\; 12+9\sqrt{3} \qquad\textbf{(B)}\; 18+6\sqrt{3} \qquad\textbf{(C)}\; 12+12\sqrt{2} \qquad\textbf{(D)}\; 30 \qquad\textbf{(E)}\; 32</math> |
==Solution== | ==Solution== | ||
Revision as of 16:20, 3 March 2015
Problem
In 
, 
and 
. Squares 
and 
are constructed outside of the triangle. The points 
, 
, 
, and 
lie on a circle. What is the perimeter of the triangle?
Solution
See Also
| 2015 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 18 |
Followed by Problem 20 |
| 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 | |
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