Question 14
$R$ is a point on a segment $CQ$ with $CR=4$ cm. A line perpendicular to $CQ$ intersect the circles with diameters $CR$ and $CQ$ at $A$ and $B$ respectively, with $A$ and $B$ on opposite sides of $CQ$. If the circumradius of triangle $ABC$ is $\sqrt6$ cm, find the length, in cm, of $CQ$.
Figure note: The complete original diagram is taken from the official Traditional Chinese edition; the supplied English PDF truncates the lower drawing and omits some labels. The English wording and the square-root radius are retained.
Submission guidance: Include a detailed explanation, as required for Section B.
Figure note: The complete original diagram is taken from the official Traditional Chinese edition; the supplied English PDF truncates the lower drawing and omits some labels. The English wording and the square-root radius are retained.
Submission guidance: Include a detailed explanation, as required for Section B.