Difference between revisions of "1969 AHSME Problems/Problem 10"

Latest revision as of 03:01, 7 June 2018

Problem

The number of points equidistant from a circle and two parallel tangents to the circle is:

$\text{(A) } 0\quad \text{(B) } 2\quad \text{(C) } 3\quad \text{(D) } 4\quad \text{(E) } \infty$

Solution

$[asy] draw(circle((0,0),100)); draw((-300,100)--(300,100),Arrows); draw((-300,-100)--(300,-100),Arrows); draw((-300,0)--(300,0),dotted,Arrows); dot((-200,0)); dot((0,0)); dot((200,0)); draw((-200,100)--(-200,-100),dotted); draw((200,100)--(200,-100),dotted); [/asy]$ The distance between the two parallel tangents is the length of the circle's diameter, so the distance from a point that satisfies the conditions and the two tangents is the length of the circle's radius. From the diagram, there are $\boxed{\textbf{(C) } 3}$ points that satisfies the conditions.

1969 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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Difference between revisions of "1969 AHSME Problems/Problem 10"

Latest revision as of 03:01, 7 June 2018

Problem

Solution

See also

@@ Line 10: / Line 10: @@
 == Solution ==
-<math>\fbox{C}</math>
+<asy>
+draw(circle((0,0),100));
+draw((-300,100)--(300,100),Arrows);
+draw((-300,-100)--(300,-100),Arrows);
+draw((-300,0)--(300,0),dotted,Arrows);
+dot((-200,0));
+dot((0,0));
+dot((200,0));
+draw((-200,100)--(-200,-100),dotted);
+draw((200,100)--(200,-100),dotted);
+</asy>
+The distance between the two parallel tangents is the length of the circle's diameter, so the distance from a point that satisfies the conditions and the two tangents is the length of the circle's radius.  From the diagram, there are <math>\boxed{\textbf{(C) } 3}</math> points that satisfies the conditions.
 == See also ==