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Answer

`2sqrt(3)` sq unit

Explanation

Equation of tangent at the point `(1,sqrt(3))` to the curve
`x^(2)+y^(2)=4 " is " x+ sqrt(3)y=4 `
whose X-axis intercept(4,0).

Thus, area of `triangle` formed by `(0,0)(1, sqrt(3))` and (4,0)
` =(1)/(2)|(0,0,1),(1,sqrt(3),1),(4,0,1)|-(1)/(2)|(0-4sqrt(3))|-2sqrt(3) `sq units