Answer :
In order to determine the length of the string on segment ER so that E’ is wrapped onto point Q, we must first consider the properties of circles and their associated angles and arc lengths. Let’s take a look at what we know: Circumference of a circle: C = 2πr
= θrWe also know that the string is wrapping around the circumference of circle D, so we can use the circumference formula to find the length of the string required. However, we need to find the radius of circle D first. To do this, we can use the Pythagorean theorem since we know the length of segments EQ and QD, as shown below:EQ2 + QD2
= ED2 (by the Pythagorean theorem)EQ2 + QD2 = 102 + 82
= 164EQ
= √164
= 4√41 (approx.)Since EQ is a radius of circle D, we can now find the circumference of circle D:C
= 2πr
= 2π(4√41) ≈ 25.24The string is wrapping around the circle from endpoint E to endpoint R, but we only need the length of the string on segment ER. To find this length, we need to subtract the arc lengths of segments EQ and QR from the circumference of circle
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