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Topic: Finding a Tangent Point on a Circle
Replies: 1   Last Post: Oct 21, 1999 9:44 AM

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Jon Roberts

Posts: 47
Registered: 12/6/04
Re: Finding a Tangent Point on a Circle
Posted: Oct 21, 1999 9:44 AM
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Hi Chris,

Since the circle's radii form right angles with line joining the external point
to the points of tangency at the points of tangency, the quadrilateral formed by
joning the centre to one tangent point to the external point to the second
tangency point and so back to the centre is a kite in which the opposite equal
angles are both 90 degrees. Thus it is a cyclic quadralateral and furthermore
the line from the original circle's centre to the external point is a diameter
of this kite's circumcircle. Thus the two points of tangency are the
intersections of the original circle and the circle centred at the midpoint of
the line joining the original circle's centre to the external point, and with a
radius of half its length.


Jon Roberts

Chris wrote:

> Can anyone tell me (if it exists) the formula to find a tangent point on
> a Circle at (x,y) with radius R from any known point outside the Circle?
> I've tried to accomplish this using the method outlined in this newsgroup
> posting "Coordinate (I think) vs Polar Angles". It is best if you start
> with the "Coordinate (I think) vs Polar Angles w/ correct graphic" posted by
> Charlie.
> All Help is Greatly Appreciated,

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