In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ? 
Options: a ) 135 , b ) 125 , c ) 120 , d ) 110 , e ) 140
a

Problem: the length and the breadth of a rectangle are in the ratio of 3 : 2 respectively . if the sides of the rectangle are extended on each side by 1 metre , the ratio of length to breadth becomes 10 : 7 . find the area of the original rectangle in square metres . 
Options: ['a ) 256', 'b ) 150', 'c ) 280', 'd ) data inadequate', 'e ) none of these']
e

Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9 , 40 and 41 ? 
Options: a ) 6 , b ) 4 , c ) 24.5 , d ) 20.5 , e ) 12.5

d