How do you solve tangent problems in geometry?

Answer 1

You find the ( x,y) coordinates of the point where the tangent line just touches the circumference of a circle.

The tangent line will have the straight line eq'n ( y = mx + c)

The circle circumference will have the circle eq'n ( x^(2) + y^(2) = r^(2)

The way to do it is to square up the straight line eq;b/

y^(2) = (mx + c)^(2) = ( (mx)^(2) + 2mxc + c^(2) )

Note how the RHS is squared up.

Subtract to eliminate 'y'

Then you have only 'x' to be solved. Since 'x' is squared 'x^(2)' , and the 'm' , 'r' and 'c' are constants, you can form a quadratic eq'n, to solve for 'x'.

Once solved you substitute 'x' back into either eq'n to find 'y'.

Answer 2

The answer depends on the precise nature of the problem.