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November 29th, 2009, 06:46 AM   #1
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tangent

calculate the length of the tangent to the circle $\displaystyle x^2+y^2-5x-5=0$ from the point (5,4).

Last edited by skipjack; February 28th, 2018 at 01:40 PM.
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November 29th, 2009, 07:05 AM   #2
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Re: tangent

How about as easier problem to study?
Consider the circle centered at (3,0) with radius = 2, and the point ( -1, -3).
Draw the circle and the point.
Draw the segment connecting the center of the circle and the point.
Find the length of this segment using the distance formula or pythagorean theorem.
There are two tangents to the circle that pass through ( -1, 3). Draw at least one of those, keeping in mind that the angle between the circle and the line is 90 degrees.
Draw the radius (not just any radius...) between the center of the circle and the point of tangency (where the line touches the circle).

You should now have a RIGHT TRIANGLE. One of the legs is just 2, since it's the radius of the circle. The hypotenuse is the segment connecting the center of the circle and the given point outside the circle. In my example, that distance (length) should be 5.

Your task is to find the length of the other leg of this RIGHT TRIANGLE, and you already know two sides.
Good luck.

p.s. great to see that even drumming gods need help in math!
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November 29th, 2009, 07:23 AM   #3
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Re: tangent

Great help, thanks. I am a fan of him .. hihi.

Last edited by skipjack; February 28th, 2018 at 01:41 PM.
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