1992 年

If $A+B+C=180^\circ$, then $1+\cos A\cos(B+C)=$

The figure shows the graph of the function

Which of the following equations has/have solutions? I. $2\cos^2\theta-\sin^2\theta=1$ II. $2\cos^2\theta-\sin^2\theta=2$ III. $2\cos^2\theta-\sin^2\theta=3$

In the figure, $O$ is the centre of the circle. Find $\theta$.

In the figure, $ABCD$ is a square of side $6$. If $BE=CE=5$, find $AE$.

In the figure, the circle is inscribed in a regular pentagon. $P$, $Q$ and $R$ are points of contact. Find $\theta$.

In the figure, $ST$ is a tangent to the smaller circle. $ABC$ is a straight line. If $\angle TAD=2x$ and $\angle DPC=3x$, find $x$.

If the two lines $2x-y+1=0$ and $ax+3y-1=0$ do not intersect, then $a=$

If $0<k<h$, which of the following circles intersect(s) the $y$-axis? I. $(x-h)^2+(y-k)^2=k^2$ II. $(x-h)^2+(y-k)^2=h^2$ III. $(x-h)^2+(y-k)^2=h^2+k^2$

If the line $y=mx+3$ divides the circle $x^2+y^2-4x-2y-5=0$ into two equal parts, find $m$.