幾何與角

In the figure, I, II and III are equilateral triangles. Area of I : Area of II : Area of III $=$

In the figure, $C$ is the centre of the circle. $ABCD$ is a straight line. $AQR$ touches the circle at $Q$. If $\angle DAR=20^\circ$, then $\angle DQR=$

In the figure, $DE\parallel BC$ and $AB\parallel EF$. If $AE:EC=1:2$, then area of $\triangle ADE$ : area of parallelogram $BFED=$

In the figure, $x=$

In the figure, $ABC$, $ACD$, $ADE$ and $AEF$ are right angled isosceles triangles. If $AB=BC=1$, how long is $AF$?

In the figure, $A$, $B$, $C$, $D$ and $E$ lie on a circle. $AC$ intersects $BE$ at $K$. $\angle ACD=100^\circ$ and $\angle CDE=130^\circ$. If $BE\parallel CD$, then $\angle ACB=$

If the five interior angles of a convex pentagon form an A.P. with a common difference of $10^\circ$, then the smallest interior angle of the pentagon is

$DA$ 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 $\text{cm}^2$.