<p>Points <img alt="$A$" height="13" src="https://latex.artofproblemsolving.com/0/1/9/019e9892786e493964e145e7c5cf7b700314e53b.png" width="13" /> and <img alt="$B$" height="12" src="https://latex.artofproblemsolving.com/f/f/5/ff5fb3d775862e2123b007eb4373ff6cc1a34d4e.png" width="14" /> lie on a <a href="https://artofproblemsolving.com/wiki/index.php/Circle" title="Circle">circle</a> centered at <img alt="$O$" height="12" src="https://latex.artofproblemsolving.com/5/1/d/51da37d984564162c87710ca27bea422f657fb73.png" width="13" />, and <img alt="$\angle AOB = 60^\circ$" height="13" src="https://latex.artofproblemsolving.com/9/0/2/9023248d6c30dddbacd640f69f9347269d9f8763.png" width="104" />. A second circle is internally <a href="https://artofproblemsolving.com/wiki/index.php/Tangent" title="Tangent">tangent</a> to the first and tangent to both <img alt="$\overline{OA}$" height="15" src="https://latex.artofproblemsolving.com/3/7/c/37ca7a38f7eed488e5f646482c71b0cf56222e28.png" width="28" /> and <img alt="$\overline{OB}$" height="15" src="https://latex.artofproblemsolving.com/3/f/b/3fb5b6369d95e2d66ab4cd9acd69168b7a605c2a.png" width="29" />. What is the ratio of the area of the smaller circle to that of the larger circle?</p>

Question No: 248

Points $A$ and $B$ lie on a circle centered at $O$ , and $\angle AOB = 60^\circ$ . A second circle is internally tangent to the first and tangent to both $\overline{OA}$ and $\overline{OB}$ . What is the ratio of the area of the smaller circle to that of the larger circle?

Editorial

Tags: Algebra Geometry

Question Details