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

Revision as of 01:42, 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
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

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

Revision as of 01:42, 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>