Difference between revisions of "1966 AHSME Problems/Problem 6"

Revision as of 00:42, 26 June 2016

Problem

$AB$ is the diameter of a circle centered at $O$ . $C$ is a point on the circle such that angle $BOC$ is $60^\circ$ . If the diameter of the circle is $5$ inches, the length of chord $AC$ , expressed in inches, is:

$\text{(A)} \ 3 \qquad \text{(B)} \ \frac {5\sqrt {2}}{2} \qquad \text{(C)} \frac {5\sqrt3}{2} \ \qquad \text{(D)} \ 3\sqrt3 \qquad \text{(E)} \ \text{none of these}$

Solution

$[asy] draw(unitcircle); draw((-1,0)--(1,0)--(1/2, sqrt(3)/2)--cycle); label( "A", (-1,0), W); label( "B", (1,0), E); label( "C", (1/2, sqrt(3)/2), N); [/asy]$

$\fbox{C}$

1966 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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Difference between revisions of "1966 AHSME Problems/Problem 6"

Revision as of 00:42, 26 June 2016

Problem

Solution

See also

@@ Line 5: / Line 5: @@
 == Solution ==
+<asy>
+draw(unitcircle);
+draw((-1,0)--(1,0)--(1/2, sqrt(3)/2)--cycle);
+label( "A", (-1,0), W);
+label( "B", (1,0), E);
+label( "C", (1/2, sqrt(3)/2), N);
+</asy>
 <math>\fbox{C}</math>