Which statement correctly gives the unknown arc length and the justification for the measurement? 18 cm42 cm13 cm/to? A. The unknown arc length is 37 cm. Because the radius is 5 units shorter in length, the arc must be 5 units shorter in length.B.The unknown arc length is 30.33 cm. Because all circles are similar, the length of the arc intercepted by an angle is proportionalto the radius.OC. The unknown arc length is 42 cm. Because all circles are congruent, congruent angles must intercept congruent arcs.O D.The unknown arc length is 58.15 cm. Because arc lengths are inversely proportional to radius lengths, the smaller circle musthave a longer arc.

Answered: 18 cm to 42 cm 13 cm/ to ?

Math

Geometry

18 cm to 42 cm 13 cm/ to ?

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

Which statement correctly gives the unknown arc length and the justification for the measurement?

A. The unknown arc length is 37 cm. Because the radius is 5 units shorter in length, the arc must be 5 units shorter in length.
B.
The unknown arc length is 30.33 cm. Because all circles are similar, the length of the arc intercepted by an angle is proportional
to the radius.
OC. The unknown arc length is 42 cm. Because all circles are congruent, congruent angles must intercept congruent arcs.
O D.
The unknown arc length is 58.15 cm. Because arc lengths are inversely proportional to radius lengths, the smaller circle must
have a longer arc.

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