Apollonius Revisited Equidistance

More documents

Recommendations

Info

Distance between: Two external circles P, Q is AB, which is created by joining thecenters P&Q and removing the two radii, R & r.Thus AB= PQ-(PA+QB). AB=PQ-(R+r)= PQ " R " r!Distance between: Two circles, Q inside P, is AB, which is created by joining the centersP&Q with a ray and removing the distance between the centers and the smaller radius. r,from the bigger radius, R. Thus AB=PA-(PQ+QB)=R-(PQ+r)= PQ " R " r!Exercise: If two circles are tangent or intersecting the distance between them should bezero. Do the definitions given allow for this situation? How do the distance formulasdetect these cases?
(B) EQUIDISTANCEDefinition: A point P is equidistant to two points A and B if and only if PA=PBDefinition: Perpendicular Bisector of a segment is a line that is perpendicular to thesegment at its midpoint.Exercise: Show that perpendicular bisector of a segment is the set of all pointsequidistant from the end points of the segmentDefinition: Parabola is the set of all points on a plane that are equidistant to a point(focus) and a line (directrix)
Page 1 and 2: Apollonius Revisited:EquidistanceA
Page 3 and 4: Introduction and Motivation:Apollon
Page 5: Distance between: A circle C and a
Page 9 and 10: Research: Construct and investigate
Page 11 and 12: Equilocus of:(a)Two intersecting li
Page 13 and 14: Equilocus of: A circle C and a poin
Page 15 and 16: Equilocus of: Two external circles
Page 17 and 18: Equilocus of: Two circles D inside
Page 19 and 20: (D) Apollonius Tangency Problems: E
Page 21 and 22: LLLTask: Construct a circle tangent
Page 23 and 24: LLCTask: Construct a circle tangent
Page 25 and 26: CCLTask: Construct a circle tangent
Page 27 and 28: Challenge: Study special cases not
Page 29 and 30: (c) a point and a hyperbolaAdvanced
Page 31 and 32: - Construct the perpendicular bisec
Page 33 and 34: -Hide all but the Focus, the direct
Page 35 and 36: -Construct a segment between M and
Page 37 and 38: - This tool will be handy if, say,
Page 39 and 40: Note: The difference between the di
Page 41 and 42: -Create a movable free point M on t
Page 43 and 44: -Hide all but the loci and two poin
Page 45 and 46: -Construct E and F, the intersectio

Apollonius Revisited Equidistance

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?