An equilateral triangle and a regular hexagon are inscribed in the same circle which has a radius of $20 \mathrm{cm}$. They have $3$ vertices in common. What is the difference (in ${\mathrm{cm}}^2$) in the areas of the triangle and the hexagon?

In the given diagram, point R and Q are on PS. ÐPQT = x°, ÐRQT = (x – 50)° and ÐTUR = (x + 25°). find the value of ÐURS.

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

Read the given question and decide which of the following information is sufficient to answer the question.

What is the value of 0?

Information :

(II) 0 < q < 90°

If the interior angle of a regularpolygon is $108°$, then it is a-

1. Octagon

2. Hexagon

3. Pentagon

4. Tetragon 

The two circles with radii $6 cm$ and $3 cm$ centred at the point $P$ and $Q$ respectively. A transverse common tangent $AC$ to the both circles cuts line Joining $P$ and $Q$ at the point $B$ such that $AB = 8 cm$. Calculate the length (in cm.) of $PQ$.