In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of

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In a circle of diameter 40 cm, the length of a chord is 20...

Key Concepts

Arc Length

Arc length is the measure of the distance along the curved part of the circle defined by a central angle. It is calculated by multiplying the radius of the circle by the central angle in radians, reflecting the proportionality between the angle and the total circumference of the circle.

Central Angle

The central angle is an angle with its vertex at the center of the circle, and its sides (radii) extend to the circumference. This angle is critical in defining both the corresponding chord and the arc and allows for the application of trigonometric relationships to connect the measures of arcs and chords.

Trigonometric Relationships in Circle Geometry

Trigonometric relationships, such as the sine function in the chord length formula, connect the angle measures and side lengths in circle geometry. These relationships enable calculations that relate the chord length, central angle, and subsequently the arc length, making them essential tools in solving problems related to circles.

Circle

A circle is a set of all points in a plane that are equidistant from a given center point. Its properties, such as the radius, diameter, and circumference, form the basis for understanding more complex relationships in circle geometry, including chords, arcs, and angles.

Chord

A chord is a straight line segment whose endpoints both lie on the circle. Its length is determined by its position relative to the circle’s center and the central angle it subtends, and it is directly related to trigonometric functions that link angles with distances in the circle.

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