The North part of the city has two perfectly circular and concentric ring roads (see figure below), the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Find the ratio of the sum of lengths of all chord roads to the length of outer ring road?

The North part of the city has two perfectly circular and concentric ring roads (see figure below), the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Find the ratio of the sum of lengths of all chord roads to the length of outer ring road?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

The North part of the city has two perfectly circular and concentric ring roads (see figure below), the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E₁, the east end point of OR to N₂, the north end point of IR; from N₁, the north end point of OR to W₂, the west end point of IR; from W₁, the west end point of OR, to S₂, the south end point of IR; and from S₁ the south end point of OR to E₂, the east end point of IR. Find the ratio of the sum of lengths of all chord roads to the length of outer ring road?

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