Prove algebraically that the straight line with the equation x-2y=10 is a tangent to the circle with the equation x² + y² = 20.
a) Show that the line and circle intersect at a single point
b) Show that the line and circle have the same slope at their point of intersection
c) Show that the distance between the line and the center of the circle equals the radius
d) Show that the line is perpendicular to the radius at their point of intersection
