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Difference between revisions of "1993 AHSME Problems/Problem 27"

(Created page with "== Problem == <asy> draw(circle((4,1),1),black+linewidth(.75)); draw((0,0)--(8,0)--(8,6)--cycle,black+linewidth(.75)); MP("A",(0,0),SW);MP("B",(8,0),SE);MP("C",(8,6),NE);MP("P",(...")
 
Line 5: Line 5:
 
MP("A",(0,0),SW);MP("B",(8,0),SE);MP("C",(8,6),NE);MP("P",(4,1),NW);
 
MP("A",(0,0),SW);MP("B",(8,0),SE);MP("C",(8,6),NE);MP("P",(4,1),NW);
 
MP("8",(4,0),S);MP("6",(8,3),E);MP("10",(4,3),NW);
 
MP("8",(4,0),S);MP("6",(8,3),E);MP("10",(4,3),NW);
 +
MP("->",(5,1),E);
 
dot((4,1));
 
dot((4,1));
 
</asy>
 
</asy>
−
The sides of <math>\triangle ABC</math> have lengths <math>6,8,\text{ and } 10</math>. A circle with center <math>P</math> and radius <math>1</math> rolls around the inside of <math>\triangle ABC</math>, always remaining tangent to at least one side of the triangle. When <math>P</math> first returns to its original position, through what distance has <math>P</math> traveled?
+
The sides of <math>\triangle ABC</math> have lengths <math>6,8,</math> and <math>10</math>. A circle with center <math>P</math> and radius <math>1</math> rolls around the inside of <math>\triangle ABC</math>, always remaining tangent to at least one side of the triangle. When <math>P</math> first returns to its original position, through what distance has <math>P</math> traveled?
  
 
<math>\text{(A) } 10\quad
 
<math>\text{(A) } 10\quad
Line 16: Line 17:
  
 
== Solution ==
 
== Solution ==
−
<math>\fbox{}</math>
+
<math>\fbox{B}</math>
  
 
== See also ==
 
== See also ==

Revision as of 21:41, 26 September 2014

Problem

[asy] draw(circle((4,1),1),black+linewidth(.75)); draw((0,0)--(8,0)--(8,6)--cycle,black+linewidth(.75)); MP("A",(0,0),SW);MP("B",(8,0),SE);MP("C",(8,6),NE);MP("P",(4,1),NW); MP("8",(4,0),S);MP("6",(8,3),E);MP("10",(4,3),NW); MP("->",(5,1),E); dot((4,1)); [/asy] The sides of $\triangle ABC$ have lengths $6,8,$ and $10$. A circle with center $P$ and radius $1$ rolls around the inside of $\triangle ABC$, always remaining tangent to at least one side of the triangle. When $P$ first returns to its original position, through what distance has $P$ traveled?

$\text{(A) } 10\quad \text{(B) } 12\quad \text{(C) } 14\quad \text{(D) } 15\quad \text{(E) } 17$

Solution

$\fbox{B}$

See also

1993 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 26 		Followed by
Problem 28
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 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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