Answered

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In the two concetric circles on the right, angle CON intercepts arc CN and arc RW.

a. Are the degree measures of arc CN and arc RW equal? Why?
b. Are the lengths of the two arc equal? Explain your answer.

Sagot :

Concentric circles are circles with the same center;  Try visualizing a circle inside a bigger circle having the same center.

If Point O is the center of the given circles, and angles CON and ROW are central angles, with O as their vertices, and angle CON intercepts both arcs CN and RW, hence:

a.  The degree measures of arcs intercepted by the central angles are congruent, because the central angles that intercept both arcs CN and RW have the same degree measures.  (Proof:  Measure of central angle is equal to the measure of the arc it intercepts).

b). No.  Because the two circles don't have the same radius. In determining the arc length, radius is considered.  EXCEPT, when the two circles are overlapping circles with the same area and circumference.
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