Solve the following mathematical problems:

The length of a tangent from a point A at distance 5cm from the center of the circle is 4cm. Find the radius of the circle

Solve the following mathematical problems:

A novelist earned Tk. 1,00,000 from royalties on her book. She paid 20% income tax on the royalties. She invested Tk. 50,000 at one rate and the rest at a rate that was 1% lower, earning 6,100 taka annual interest on the two investments. What was the lower rate?

Solve the following mathematical problems:

A working couple earned a total of Tk. 43,520. The wife earned Tk. 640 per day, the husband earned Tk. 560 per day. If the total number of days worked by both was 72, formulate system of equation and solve the system to find the number of days worked by each.

Solve the following mathematical problems:

A man's salary in 2015 was Tk. 20,000 per annul and it increased by 10% each year. Find how much he earned in the years 2015 to 2017 inclusive.

Solve the following mathematical problems:

Prove that the sum of the odd numbers from 1 to 125 inclusive is equal to the sum of the odd numbers from 169 to 209 inclusive.

Solve the following mathematical problems:

$if a=x{y}^{p-1},b=x{y}^{q-1},c=x{y}^{r-1} and p+q+r=3, then prove that a^{q-r}\times b^{r-p}\times c^{p-q}=1$