2001 年

In the figure, $PC$ is a vertical pole standing on the horizontal ground $ABC$. $D$ is a point on line $AB$. If $\angle BCA=\angle CDB=90^\circ$, $AC=3\text{ m}$, $BC=4\text{ m}$ and $PC=5\text{ m}$, find $\tan\theta$.

In the figure, $ABCD$ and $AGFE$ are straight lines. Find $CF$.

Consider the circle $x^2+y^2-8x-6y+21=0$. Find the equation of the chord whose mid-point is $(5,2)$.

In the figure, the inscribed circle of $\triangle OPQ$ touches $PQ$ at $R$. Find the coordinates of $R$.