Question 194444: Find the coordinates of the center of a circle that is tangent to the y-axis and intersects the x-axis at (8,0) and (18,0). I don't really understand how to draw the picture and how to start it.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! tangent means that the circle is resting against (touching) the y-axis
since the circle is touching the y-axis, the center must be midway between the points where it crosses the x-axis
so the x-coordinate of the center is 13
because the circle is tangent to the y-axis, the radius is 13
the segment of the x-axis that is cut by the circle, forms a chord of the circle
the length of the chord is 10 (18-8)
half of the length of the chord is 5
the radius is 13, half of the chord is 5
using Pythagoras, the distance from the center to the chord is 12 (13^2 - 5^2 = 12^2)
so the center of the circle is 12 units from the x-axis
since it could be above OR below, the center is either (13,12) OR (13,-12)
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