(Two concentric circles are shown)The smaller circle's circumference is 10pi. The chord's length is 24. What is the diameter of the larger circle.
but we need the figure to solve for this.
A DART BOARD AS 4 rings the center ring as a diameter of 10 cm.each ring as a lenght of 3cm. what is the area of the third ring
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To find the diameter of the larger circle, we need to use the relationship between the diameter of a circle and the length of a chord. Here's how you can find the diameter:
1. Start by finding the radius of the smaller circle. Since the circumference of the smaller circle is given as 10π, we can use the formula C = 2πr, where C is the circumference and r is the radius.
10π = 2πr
Divide both sides of the equation by 2π:
10π / 2π = r
Simplifying the expression:
5 = r
Therefore, the radius of the smaller circle is 5 units.
2. Now, let's find the radius of the larger circle. Since the smaller circle is concentric (having the same center) with the larger circle, the radius of the larger circle is equal to the sum of the radius of the smaller circle and the length of the chord (since the chord bisects the diameter of the larger circle).
Radius of the larger circle = Radius of smaller circle + Length of the chord
Radius of the larger circle = 5 + 24 = 29 units.
3. Finally, to find the diameter of the larger circle, we can double the radius:
Diameter of the larger circle = 2 * Radius of the larger circle
= 2 * 29
= 58 units.
Therefore, the diameter of the larger circle is 58 units.