a. Are all circles similar?b. If two circles have radii 9 and 12, what is the ratio of the circumferences? Of the areas?

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Warenberg56i · Accepted Answer

Step 1a) The shape of the circles are always round and shape of all the circles are same.The size of the circles may be different from the other circles depends upon the length of radius.Thus, all the circles are similar because of their same shape.Step 2b) To find:The ratio of circumferences and ratio of areas of the circle having radii 9 and 12 units.Concept used:The circumference of the circle having radius r isC=2πrHere, C is circumference of the circle.The area of the circle having radius r is A=πr2Here, A is area of the circle.Step 3Calculation:Let the circumference of the circle having radius 9 is C1 and circumference of the circle of radius 12 is C2The ratio of the circumferences C1 to C2 can be obtained as,C1C2=2π(9)2π(12)=34Thus, the ratio of circumferences are 34Let the Area of the circle having radius 9 is A1 and circumference of the circle of radius 12 is A2.The ratio of the circumferences A1 to A2 can be obtained as,A1A2=π(9)2π(12)2=81144=916Thus, the ratio of areas are 916Thus, the ratio of circumferences are 34 and the ratio of areas are 916.

a. Are all circles similar? b. If two circles have radii

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