Prove that for a point z outside the circle C with center zo (Figure 3.2.18(b), the following construction finds the symmetry point of z. (1) Construct the circle having diameter z0z. Let t be a point of intersection of the two circles. (2) Construct the perpendicular to z0z through t. Let z* be the intersection of this perpendicular with segment z0z.

Prove that for a point z outside the circle C with center zo (Figure 3.2.18(b), the following construction finds the symmetry point of z. (1) Construct the circle having diameter z0z. Let t be a point of intersection of the two circles. (2) Construct the perpendicular to z0z through t. Let z* be the intersection of this perpendicular with segment z0z.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(1)
(4)
(1)
(3)
Zo
(2)
C
(2)
(a)
(b)
Figure 3.2.18: Constructing the symmetric point (a) if z is inside the circle
of inversion; (b) if z is outside the circle of inversion.
3.
Constructing the symmetric point to z when z is outside the circle of
inversion.
Prove that for a point z outside the circle C with center zo (Figure 3.2.18(b)),
the following construction finds the symmetry point of z. (1) Construct the
circle having diameter zoz. Let t be a point of intersection of the two circles.
(2) Construct the perpendicular to z0z through t. Let z* be the intersection
of this perpendicular with segment z0z.

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