Three regular hexagons are drawn such that their diagonals cut each other at the same point and area $A_1:A_2:A_3=1:2:3$. Then the ratio of the length of the sides of the regular hexagons (from the smallest to the largest) is:

Two circles $C_1$ and $C_2$ of radius $2$ and $3$ respectively touch each other as shown in the figure. If $AD$ and $BD$ are tangents then the length of $BD$ is

A right angled triangle is drawn on a plane such that sides adjacent to right angle are $3 cm$ and $4 cm$. Now three semi-circles are drawn taking all three sides of the triangle as diameters respectively (as shown in the figure). What is the area of the shaded regions $A_1+A_2$

In the given figure

$AB=20$

$BC=15$

$CA=19$

Calculate $a,b,c$

In the figure given below, $AB$ is perpendicular to $ED$. $\angle CED={75}^o$ and $\angle ECF={30}^o$. What is the measure of $\angle ABC$?