# Difference between revisions of "1954 AHSME Problems/Problem 46"

Line 1: | Line 1: | ||

+ | == Problem 46== | ||

+ | |||

+ | In the diagram, if points <math>A, B</math> and <math>C</math> are points of tangency, then <math>x</math> equals: | ||

+ | |||

+ | <asy> | ||

+ | unitsize(5cm); | ||

+ | defaultpen(linewidth(.8pt)+fontsize(8pt)); | ||

+ | dotfactor=3; | ||

+ | pair A=(-3*sqrt(3)/32,9/32), B=(3*sqrt(3)/32, 9/32), C=(0,9/16); | ||

+ | pair O=(0,3/8); | ||

+ | draw((-2/3,9/16)--(2/3,9/16)); | ||

+ | draw((-2/3,1/2)--(-sqrt(3)/6,1/2)--(0,0)--(sqrt(3)/6,1/2)--(2/3,1/2)); | ||

+ | draw(Circle(O,3/16)); | ||

+ | draw((-2/3,0)--(2/3,0)); | ||

+ | label("$A$",A,SW); | ||

+ | label("$B$",B,SE); | ||

+ | label("$C$",C,N); | ||

+ | label("$\frac{3}{8}$",O); | ||

+ | draw(O+.07*dir(60)--O+3/16*dir(60),EndArrow(3)); | ||

+ | draw(O+.07*dir(240)--O+3/16*dir(240),EndArrow(3)); | ||

+ | label("$\frac{1}{2}$",(.5,.25)); | ||

+ | draw((.5,.33)--(.5,.5),EndArrow(3)); | ||

+ | draw((.5,.17)--(.5,0),EndArrow(3)); | ||

+ | label("$x$",midpoint((.5,.5)--(.5,9/16))); | ||

+ | draw((.5,5/8)--(.5,9/16),EndArrow(3)); | ||

+ | label("$60^{\circ}$",(0.01,0.12)); | ||

+ | dot(A); | ||

+ | dot(B); | ||

+ | dot(C);</asy> | ||

+ | |||

+ | <math> \textbf{(A)}\ \frac{3}{16}"\qquad\textbf{(B)}\ \frac{1}{8}"\qquad\textbf{(C)}\ \frac{1}{32}"\qquad\textbf{(D)}\ \frac{3}{32}"\qquad\textbf{(E)}\ \frac{1}{16}" </math> | ||

==Solution 1== | ==Solution 1== |

## Revision as of 17:01, 27 April 2020

## Problem 46

In the diagram, if points and are points of tangency, then equals: