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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
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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(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.
Transcribed Image Text:(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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