To nd a formula for the length of the side of a regular inscribed polygon of 2n sides in terms of the length of the side of the regular polygon of n sides, proceed as follows. Let PR = S, be the side of a regular n-gon inscribed in a circle of radius 1. Through the center O of the circle, draw a perpendicular to PR, bisecting PR at T and meeting the circle at Q; then PQ = QR = S2n are sides of the inscribed regular 2n-gon. Prove that |D (a) OT = OR² – TR² = 1 – (1-) 2 4 – S? (b) QT° = (1 – OT) 2 (c) S, = QT + TR² = 2 – 4 – S;. Q S2n R P S.

To nd a formula for the length of the side of a regular inscribed polygon of 2n sides in terms of the length of the side of the regular polygon of n sides, proceed as follows. Let PR = S, be the side of a regular n-gon inscribed in a circle of radius 1. Through the center O of the circle, draw a perpendicular to PR, bisecting PR at T and meeting the circle at Q; then PQ = QR = S2n are sides of the inscribed regular 2n-gon. Prove that |D (a) OT = OR² – TR² = 1 – (1-) 2 4 – S? (b) QT° = (1 – OT) 2 (c) S, = QT + TR² = 2 – 4 – S;. Q S2n R P S.

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

To nd a formula for the length of the side of a
regular inscribed polygon of 2n sides in terms of the
length of the side of the regular polygon of n sides,
proceed as follows. Let PR = S, be the side of a
regular n-gon inscribed in a circle of radius 1.
Through the center O of the circle, draw a
perpendicular to PR, bisecting PR at T and meeting
the circle at Q; then PQ = QR = S2n are sides of the
inscribed regular 2n-gon. Prove that
|D
(a) OT = OR² – TR² = 1 –
(1-)
2
4 – S?
(b) QT° = (1 – OT)
2
(c) S, = QT + TR² = 2 –
4 – S;.
Q S2n
R
P
S.

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