View source for 1981 AHSME Problems/Problem 23

==Problem==
Equilateral <math>\triangle ABC</math> is inscribed in a circle. A second circle is tangent internally to the circumcircle at <math>T</math> and tangent to sides <math>AB</math> and <math>AC</math> at points <math>P</math> and <math>Q</math>. If side <math>BC</math> has length <math>12</math>, then segment <math>PQ</math> has length

<math>\textbf{(A)}\ 6\qquad\textbf{(B)}\ 6\sqrt{3}\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 8\sqrt{3}\qquad\textbf{(E)}\ 9</math>