Answer:
175 sq units
Step-by-step explanation:
The equation of the circle is
[tex]x^2+y^2 = 50[/tex]
Tangent at point (1,7) will have slope equal to its derivative value
Differentiate to get
[tex]2x+2yy1 = 0\\y1 = \frac{-x}{y} =\frac{-1}{7}[/tex]
Using point slope formula
[tex]y-7 = \frac{-1}{7} (x-1)\\y = \frac{-1}{7}x+ \frac{50}{7}[/tex]
this line cuts x axis at (50,0) P
The triangle OAP has vertices equal to (0,0) (1,7) and (50,0)
The triangle has base as OP = 50 units
Height = distance of A from x axis = 7
Area = [tex]\frac{1}{2} bh\\= 175[/tex] sq units
