1971
Problem - 3121
$DEB$ is a chord of a circle such that $DE=3$ and $EB=5 .$ Let $O$ be the center of the circle. Join $OE$ and extend $OE$ to cut the circle at $C.$ Given $EC=1,$ find the radius of the circle
Extending $CO$ to meet the circle at $P.$ Let the radius be $r$. Then, by the power of a point therefore,
$$EP\cdot CE=BE\cdot ED \implies (2r-1)\times 1=3\times 5\implies r=\boxed{8}$$