1990 年

In the figure $AB$, $AC$ and $BC$ are three tangents touching the circle at $D$, $E$ and $F$ respectively. If $AC=24$, $BC=18$ and $\angle ACB=90^\circ$, find the radius of the circle.

In the figure, $\triangle PTQ$, $\triangle SQR$ and $\triangle RUT$ are equilateral triangles. Which of the following is/are true? I. $\triangle UPT\cong\triangle RQT$ II. $PU=QS$ III. $PQSU$ is a parallelogram