Two circles touch each other externally. The sum of their areas is $130 \pi \text{ cm}^2$ and the distance between their centres is $14 \text{ cm}$. The radius of the smaller circle is . . . . . . $\text{cm}$.

The ratio of the $3$ angles of a quadrilateral is $13: 9: 5$. The value of the $4^{th}$ angle of the quadrilateral is $36^{\circ}$. What is the difference between the largest and the second smallest angles of the quadrilateral? (in $^{\circ}$)

Height of an equilateral triangle is $6 \, cm$. Find its side? (in $cm$)

In a triangle $ABC$,$AB + BC = 12 \text{ cm}$,$BC + CA = 14 \text{ cm}$,and $CA + AB = 18 \text{ cm}$. Find the radius of the circle (in $\text{cm}$) which has the same perimeter as the triangle.

The length and breadth of a rectangular field are in the ratio $5: 3.$ If the cost of cultivating the field at $25$ $paise$ per square metre is ₹ $6000,$ then find the dimensions of the field.

$3$ horses are tethered at $3$ corners of a triangular plot of land having sides $20 \, m$,$30 \, m$,and $40 \, m$,each with a rope of length $7 \, m$. The area (in $m^2$) of the region of this plot,which can be grazed by the horses,is (Use $\pi = \frac{22}{7}$)