First slide
Definition of a circle
Question

 A circle touches the line 4x+3y=12 at D and positive x,y axes. Let DE be 

 diameter of circle and OE intersect the line at F, then [4DF] is equal to ([.] is GIF)  (Provided OE<OD and O being origin ).

Difficult
Solution

 Equation of circle is x2+y22x2y+1=0D is 95,85

 taking (1,1) as and point E is 15,25

 OE has equation y=2x

F is 65,125DF=1

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