The equation of the given circle is $\rm x^2 + y^2 = 100 \Rightarrow x^2 + y^2 = 10^2$. It is in the standard form, so its center is at (0,0). Its radius is 10 units.

TANGENT TO CIRCLE

The equation of tangent to a standard circle is given by: $\rm xx_1 + yy_1 = a^2$ where $\rm (x_1, y_1)$ are the points through which the tangent passes. And, a is the radius of the circle.

Here, $\rm (x_1, y_1) = (1,2)$ and $\rm a = 10$

Hence,

$\rm x (1) + y (2) = 10^2$

$\rm or, x + 2y = 100$

$\rm or, x + 2y = 100$

$\rm \therefore x + 2y - 100 = 0$

Hence, the required equation of the tangent to the circle is x + 2y - 100 = 0.

NORMAL TO CIRCLE

The equation of normal to a standard circle is given by: $\rm x_1 y = y_1 x$, where $\rm (x_1, y_1)$ are the points through which the normal passes.

Here, $\rm (x_1, y_1) = (1,2)$

Hence,

$\rm (1) y = (2) x$

$\rm y = 2x$

$\rm \therefore 2x - y = 0$

Hence, the required equation of the normal to the circle is 2x - y = 0.