Question 1
SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
Two circles with centres $A$ and $B$ are externally tangent at $C$. The line $DF$ is tangent to them at $D$ and $F$. Their radii are 2 cm and 3 cm, respectively. Find $DC/FC$.
Two circles with centres $A$ and $B$ are externally tangent at $C$. The line $DF$ is tangent to them at $D$ and $F$. Their radii are 2 cm and 3 cm, respectively. Find $DC/FC$.