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Which statement correctly gives the unknown arc length and the justification for the measurement?A. The unknown arc length is 42 cm. Because all circles are congruent, congruent angles must intercept congruent arcs.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.C. 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.D. 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.

Which Statement Correctly Gives The Unknown Arc Length And The Justification For The MeasurementA The Unknown Arc Length Is 42 Cm Because All Circles Are Congru class=

Sagot :

All circles are similar. This means that the ratio of the radius to the circumference of every circle is equal.

For a cut-out of a circle, the same ratio holds, as long as the angle of the circumference from the center of the circle is preserved.

From the image provided, we have that the angle is the same in both circles. Hence, we have that:

[tex]\frac{42}{18}=\frac{x}{13}[/tex]

taking x as the circumference of the unknown

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