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Parts of Circle: Definition and Examples | EDU.COM

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Parts of Circle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Parts of CircleParts of Circle: Definition and ExamplesTable of ContentsParts of a Circle Definition of Circle and Its Components

A circle is a round two-dimensional plane figure formed by a set of points that are at a fixed distance from a central point in the same plane. Based on their shape and position, circles have different parts including the center (the fixed point), radius (the fixed distance from center to boundary), diameter (a line through the center connecting two points on the circumference), circumference (the total distance around the circle), chord (a line segment joining two points on the circumference), arc (a segment of the circumference), tangent (a line touching the circle at a single point), secant (the extension of a chord), and sector (a portion created by two radii).

A circle has three distinct regions: the interior region (inside the circle), the exterior region (outside the circle), and points on the circle itself (the boundary). The circumference of a circle can be calculated using the formula 2πr2\pi r2πr, where rrr is the radius. Important facts about circles include: the diameter is the longest chord, a full circle measures 360 degrees, and dividing the circumference by the diameter always gives the value of π\piπ (approximately 3.14 or 227\frac{22}{7}722​).

Examples of Circle Calculations Example 1: Finding the Radius from a Given Diameter Problem:

Find the radius of a circle with a diameter of 12.512.512.5 inches.

Step-by-step solution:

Step 1, Look at what we know. We have the diameter of the circle which equals 12.512.512.5 inches.

Step 2, Remember the relationship between radius and diameter. The radius is half of the diameter.

Step 3, Calculate the radius by dividing the diameter by 222.

Radius = Diameter ÷ 222 Radius = 12.512.512.5 inches ÷ 222 = 6.256.256.25 inches

Step 4, Write the final answer. The radius of the circle is 6.256.256.25 inches.

Example 2: Calculating the Circumference with a Given Radius Problem:

Find the circumference of a coin if its radius is 777777 inches.

Step-by-step solution:

Step 1, Look at what we know. We have the radius of the circle which equals 777777 inches.

Step 2, Recall the formula for finding the circumference of a circle.

Circumference = 2πr2\pi r2πr where rrr is the radius

Step 3, Substitute the value of the radius into the formula.

Circumference = 2×227×772 \times \frac{22}{7} \times 772×722​×77

Step 4, Simplify the calculation step by step.

Circumference = 2×22×11=4842 \times 22 \times 11 = 4842×22×11=484 inches

Step 5, Write the final answer. The circumference of the coin is 484484484 inches.

Example 3: Finding the Diameter from the Circumference Problem:

Find the diameter of a circle if its circumference is 110110110 feet.

Step-by-step solution:

Step 1, Think about what we know. We have the circumference of the circle which equals 110110110 feet.

Step 2, Recall the formula for the circumference of a circle.

Circumference = 2πr2\pi r2πr, where rrr is the radius

Step 3, Rearrange the formula to find the radius first.

r=Circumference2πr = \frac{\text{Circumference}}{2\pi}r=2πCircumference​

Step 4, Remember that the diameter is twice the radius (d=2rd = 2rd=2r).

So, d=Circumferenceπd = \frac{\text{Circumference}}{\pi}d=πCircumference​

Step 5, Substitute the value and calculate.

d=1103.14=35.03d = \frac{110}{3.14} = 35.03d=3.14110​=35.03 feet

Step 6, Write the final answer. The diameter of the circle is 35.0335.0335.03 feet.

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