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.
As shown, $PQ=10$ is the diameter of a small circle tangent internally to a circle of radius $20$ and tangent to square $ABCD$. Given $AB=m+\sqrt n$, where $m,n$ are integers, find $m+n$.
Use the configuration shown: A and B lie on the large circle; PQ lies along its diameter through O, and Q is the midpoint of CD.
Enter the number only.
As shown, $PQ=10$ is the diameter of a small circle tangent internally to a circle of radius $20$ and tangent to square $ABCD$. Given $AB=m+\sqrt n$, where $m,n$ are integers, find $m+n$.
Use the configuration shown: A and B lie on the large circle; PQ lies along its diameter through O, and Q is the midpoint of CD.
Enter the number only.