The straight line meets the coordinate axes at A and B. A circle is drawn through A B, and the origin. Then, the sum of perpendicular distances from A and B on the tangent to the circle at the origin is
When the line intersects the x-axis,
Therefore, point A has coordinates
When the line intersects the y-axis
Therefore, point B has coordinates
The equation of the circle that passes through points A, B, and the origin
The radius of the circle is
Equation of the circle is:
tangent line to the circle at the origin
At the point his becomes:
The slope of the tangent line at the origin is
Since the line is horizontal, its equation is simply y = 0.
The perpendicular distance from point A to this line is simply the y-coordinate of A, which is 0, and the perpendicular distance from point B is the x-coordinate of B, which is also 0.
Therefore, the sum of the perpendicular distances from A and B on the tangent to the circle at the origin is
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