The lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to the same circle the radius of circle is??
Tangents, by definition, will be perpendicular to the radius lines meeting the circle at the point of tangency. So solve each of the two tangent equations for "y=", and read off their slopes. Use this information to find the values of the slopes of the radii.
In this case, the tangents are perpendidular, which means that they meet the circle at either end of a diameter line. Find the equation of any line perpendicular to the tangents. Find the points where this line crosses the two tangents.
Then plug these points into the Distance Formula to find the length of the diameter.
Divide by "2" to find the length of the radius.