Relative Positions Of A Line And A Circle

page revision: 0, last edited: 15 Sep 2008 08:59

Relative Positions Of A Line And A Circle

page revision: 0, last edited: 15 Sep 2008 08:59

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## Have a question?

Problem: Find the geometric locus of points from which the tangents drawn to a given circle are congruent to a given segment.

Do I understand this correctly? Let the given segment be 'a'. If I choose a point P in the plane, and draw two tangents to some circle, and mark the tangency points A and B, then if PA = PB = 'a', the point P satisfies the condition for membership of the locus of points?

If that's the case, then the problem is quite easy once one learns the solution for exercise 249.

Writing this helped me understand the nature of the problem.

I've completed all of the problems in this chapter except for the very first. Once I have some time (probably 2-3 weeks from now), I'll dedicate some time to posting solutions to exercises in chapters 2.1 and 2.2. So far, I've had a very great time learning elementary geometry with this book. If a solution set to all (or nearly all) problems existed, then I think that this would be more readily adopted by more educators, and therefore more students would receive a rich elementary geometry experience.

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