Question : ABCDEF is a regular hexagon. The side of the hexagon is 36 cm. What is the area of the $\triangle ABC$?

Option 1: $324 \sqrt{3}\ {cm}^2$

Option 2: $360 \sqrt{3} \ {cm}^2$

Option 3: $240 \sqrt{3} \ {cm}^2$

Option 4: $192 \sqrt{3} \ {cm}^2$

Question : A circle and a square have the same area. The ratio of the side of the square to the radius of the circle will be:

Option 1: $\sqrt\pi:1$

Option 2: $1:\sqrt\pi$

Option 3: $(\pi)^2:1$

Option 4: $1:\sqrt2\pi$

Question : The areas of a circle and a square are the same. The ratio of the side of the square to the radius of the circle is:

Option 1: $2\pi :1$

Option 2: $1:\sqrt{\pi}$

Option 3: $\sqrt{\pi}:1$

Option 4: $1:\pi$

Question : A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, then the radius of the circle is:

Option 1: $2 \sqrt{3} {~cm}$

Option 2: $\sqrt{19} {~cm}$

Option 3: $\sqrt{17} {~cm}$

Option 4: $3 \sqrt{2} {~cm}$

Question : The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

Option 1: $5 \sqrt{5}$ cm

Option 2: $5 \sqrt{2}$ cm

Option 3: $5$ cm

Option 4: $5 \sqrt{3}$ cm