1986 年

In $\triangle ABC$, $AB=2$, $AC=3$ and $\sin B=\dfrac{3}{4}$, then $\cos^2C=$

In the figure, $BD:DC=$

In the figure, $ABCD$ is a square. Arcs $AC$ and $BD$ are drawn with centres $D$ and $C$ respectively, intersecting at $O$. Arc $AO$ : Arc $OC=$

In the figure, $ABCD$ and $EFGH$ are two squares of side $1$. They are placed one upon the other with their centres both at $O$ to form a star with $16$ sides, each of length $x$. Find $x$.

$DA$ and $DC$ are equal chords of the circle $ABCD$. $\angle CDB=40^\circ$ and $\angle DAB=100^\circ$. $\angle ADB=$

In the figure, $AB$ and $AC$ are tangents to the circle $BCD$. If $\angle BDC=50^\circ$, then $\angle A=$

Three circles, centres $A$, $B$ and $C$ touch each other as shown in the figure. The radii of the two circles with centre $A$ and $B$ are both $1\text{ cm}$ and radius of the circle with centre $C$ is $3\text{ cm}$. Find the area of the shaded part in $\text{cm}^2$.

A circle, centre $O$, touches the sector $ABC$ internally at $D$, $E$ and $F$. $\angle C=60^\circ$ and $AC=18$. Find the radius of the circle.

In the figure, $PQ$ is a diameter and $PT$ is a tangent of the circle. $QT$ cuts the circle at $R$. Let $\angle Q=\theta$ and $PQ=x$, then $TR=$