Draw a Circle With 16 Segments

Chord of Circle

The chord of a circle is defined as the line segment joining any two points on the circumference of the circle. Information technology should be noted that the bore is the longest chord of a circle that passes through the middle of the circumvolve.

one.	What is the Chord of a Circumvolve?
2.	Properties of the Chord of a Circle
three.	Formula of Chord of Circumvolve
iv.	Theorems of Chord of a Circle
5.	FAQs on Chord of a Circumvolve

What is the Chord of a Circle?

A line segment that joins ii points on the circumference of the circle is divers as the chord of the circle. Among the other line segments that tin can be drawn in a circle, the chord is 1 whose endpoints lie on the circumference. Notice the post-obit circle to place the chord PQ. Diameter is also considered to be a chord which passes through the center of the circle.

Backdrop of the Chord of a Circle

Given beneath are a few important properties of the chords of a circle.

• The perpendicular to a chord, fatigued from the center of the circle, bisects the chord.
• Chords of a circumvolve, equidistant from the center of the circle are equal.
• At that place is one and but i circle which passes through 3 collinear points.
• When a chord of circle is fatigued, it divides the circumvolve into two regions, referred to as the segments of the circle: the major segment and the minor segment.
• A chord when extended infinitely on both sides becomes a secant.

Formula of Chord of Circle

In that location are two basic formulas to find the length of the chord of a circle:

• Chord length using perpendicular distance from the center = 2 × √(r^two − d²). Let us see the proof and derivation of this formula. In the circle given below, radius 'r' is the hypotenuse of the triangle that is formed. Perpendicular bisector 'd' is one of the legs of the right triangle. Nosotros know that the perpendicular bisector from the centre of the circumvolve to the chord bisects the chord. Therefore, half of the chord forms the other leg of the correct triangle. By Pythagoras theorem, (1/2 chord)² + d^two = r², which further gives i/2 of Chord length = √(r^two − dⁱⁱ). Thus, chord length = two × √(r² − d²)

• Chord length using trigonometry = ii × r × sin(θ/2); where 'r' is the radius of the circle and 'θ' is the angle subtended at the middle by the chord. Observe the following circle to run into the fundamental bending 'θ' subtended by the chord AB and 'r' as the radius of the circumvolve.

Theorems of Chord of a Circle

The chord of a circle has a few theorems related to it.

Theorem 1: The perpendicular to a chord, drawn from the center of the circle, bisects the chord.

Observe the following circle to understand the theorem in which OP is the perpendicular bisector of chord AB and the chord gets bisected into AP and Pb. This ways AP = Atomic number 82

Theorem ii: Chords of a circle, equidistant from the middle of the circle are equal.

Observe the following circle to empathise the theorem in which chord AB = chord CD, and they are equidistant from the center if PO = OQ.

Theorem three: For ii unequal chords of a circle, the larger chord will exist closer to the center than the smaller chord. (Diff Chords Theorem)

If we draw multiple chords in a circle starting from the diameter to both the ends, we will observe that as we motility closer to the center, the chord increases in length.

Important Notes

• The radius of a circle bisects the chord at xc°.
• When two radii join the ii ends of a chord, they course an isosceles triangle.
• The diameter is the longest chord of a circle.

Related Links:

• Circles
• Expanse of a Circumvolve
• Surface area of a Sector of a Circle
• Segment of a Circumvolve
• Arc Length

Chord of a Circle Examples

1. Example 1: In the given circle, O is the center, and AB which is the chord of circle is 16 cm. Discover the length of Advert if OM is the radius of the circumvolve.

   

   Solution:

   We know that the radius of a circle is always perpendicular to the chord of a circle and it acts equally a perpendicular bisector. Therefore, AD = 1/2 × AB = 16/two = eight. Therefore, AD = 8 cm.

2. Example 2: In the given circumvolve, O is the middle with a radius of 5 inches. Find the length of the chord AB if the length of the perpendicular drawn from the middle is four inches.

   

   Solution:

   AB is the chord of circumvolve. Since OM is perpendicular to AB, △AOM will exist a right-angled triangle. In △AOM, using the Pythagoras theorem, OA^two = OMⁱⁱ + AM². Later the transposition of terms, we go AM² = OA² - OM². On substituting the values, AM² = five² - 4² = 25 - 16 = 9. Thus, AM = √9 = iii. Since OM is the perpendicular bisector of AB, so AM = MB. Therefore, Chord AB = ii × 3 = half dozen inches

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Exercise Questions on Chord of a Circle

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FAQs on Chord of a Circumvolve

What is the Chord of a Circle in Mathematics?

The chord of a circle refers to a straight line joining two points on the circumference of the circle. The longest chord in a circle is its bore which passes through its centre.

How to Find the Chord of Circle?

Any line segment whose endpoints are on the circumference of the circle is the chord of that circle. The length of the chord of a circle can be calculated co-ordinate to the given dimensions, with the help of two methods.

• When the radius and the distance from the center of the circle to the chord is given, nosotros demand to apply the chord length formula: Chord length = 2√(r²-d²); where 'r' is the radius of the circle and 'd' is the perpendicular distance from the eye of the circle to the chord.
• When the radius and the key bending is given, we demand to use the formula, Chord length = 2 × r × Sin (θ/ii); where 'r' is the radius and 'θ' is the central angle subtended by the chord.

What is the Longest Chord of a Circumvolve?

The longest chord of a circle is its bore. It is the line that passes through the center of a circle touching two points on the circumference.

How to Find the Length of Chord of Circle with a Given Radius?

If the radius and the distance of the centre of the circumvolve to the chord are given, the chord of the circle can be calculated. We just need to employ the chord length formula: Chord length = 2√(r^two-d²), where 'r' is the radius of the circle and 'd' is the perpendicular distance from the center of the circumvolve to the chord.

What is the Human relationship Betwixt the Chord of a Circle and a Perpendicular to information technology from the Heart?

The perpendicular drawn from the center of a circumvolve to a chord bisects the chord. In other words, a line drawn through the heart of a circle to bisect a chord is perpendicular to the chord.

What is the Radius, Diameter, and Chord of a Circumvolve?

The radius of a circumvolve is the distance from the center to any indicate on the circumference. Diameter is the line segment that passes through the eye of a circle touching 2 points on the circumference of the circle. A chord is a line segment that joins whatsoever two points on the circumference of the circle.

How to Draw the Chord of a Circumvolve?

The chord of a circle can be constructed with the aid of a compass and a ruler. For instance, let the states draw a chord of length 4 inches in a circumvolve that has a radius of 2 inches.

• Mark the eye of the circle as O and using a compass draw a circle with a radius of 2 inches.
• Then, marking a point C on the circumference of the circle, and with C as the center depict an arc that cuts the circumference at another point D.
• Join C and D. CD is the required chord that measures 4 inches.

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Source: https://www.cuemath.com/geometry/Chords-of-a-circle/

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