Let the tangents at two point A and B on the circle $x^2+y^2-4x +3=0$meet at origin O (0,0). Then the area of the triangle of OAB is 

The given circle is $x^2+y^2-4x +3=0$

Equation of chord of contact of origin is $S_1=0$

Hence the equation of the chord of contact is $2x=3$

The length of the tangent from origin to the circle is $\sqrt{S_{11}}$

Hence, $OA=OB=\sqrt{3}$

Distance from origin to the chord of contact is $OM=\frac{3}{2}$

Area of the triangle $OAB$ is $\frac{1}{2}\left(2AM\right)\left(OM\right)$

Therefore, the area of the triangle $OAB$ is $\frac{1}{2}·\sqrt{3}·\frac{3}{2}=\boxed{\frac{3\sqrt{3}}{4}}$