Question 392130
A circle is given centered at (0,0)with a radius of 2.
A line cuts through the center of the circle (slope of line unknown) but the line makes an angle of pi/3 with the x axis in the fourth quadrant.
This line continues and cuts through point Q (coordinates unknown) of the circle in the fourth quadrant.
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Another line forms a tangent to the circle at point Q and is perpendicular to the original line.
this second line ( which is tangent to the circle and perpendicular to the original line) continues and crosses the x axis at some point P (coordinates unknown)
* note that both lines share a point Q which lies on the circle.
We are asked to ultimately find the coordinates of point P (x , 0)

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According to the information given, I ended with a right triangle in quadrant IV, labeled as follows"

O - center of circle
Q - point on circle where second line is tangent to circle and perpendicular to first line which goes thru origin.
P - point at which second line crosses x-axis

Angle at O - 60 deg
Angle at P - 30 deg
Angle at Q - 90 deg

Line segment OQ is equal to the radius = 2
since the reference angle of the first line is pi/3 = 60 deg, the angle at P must be 30 deg. This makes OP, the hypotenuse of the triangle twice that of OQ, being that OQ is opposite a 30 degree angle.  Therefore the hypotenuse is = 4.

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ans: The coordinates at point P is (4,0)