Instruction

1

Imagine you are given a circle with known radius R, her L chord subtends an arc φ, where φ is defined in degrees or radians. In this case, calculate

**the length****of the chord**according to the following formula: L = 2*R*sin(φ/2), substituting all known values.2

Consider a circle with center at point O and a given radius. Sought are two equal

**chords**AB and AC, having one point of intersection with the circumference (A). It is known that the angle formed by the chords, based on the diameter of the figure. Do the graphical construction of these elements in circumference. The radius from the center Of lower to points of intersection of chords A. Chords will form a triangle ABC. To determine the lengths of the same chords use properties of the isosceles triangle (AB=AC). The segments IN the OS and is (as by the condition - diameter) and are the radii of the figure, therefore, AO is a median of triangle ABC.3

According to the property of isosceles triangle, its median is also the altitude, that is, perpendicular to the base. Consider received right triangle AOB. The leg S is known and equal to half the diameter, that is, R. the Second leg of AO is also specified as a radius R. Hence, applying the Pythagorean theorem, Express the unknown side AB, which is the required chord of the circle. Calculate the final result AB = √(AO2 + ОВ2). According to the problem, the length of the second

**chord**AC equal to AB.4

For example, set to a circle with diameter D, and chord CE. Thus the known angle formed by a chord and a diameter. To calculate

**the length****of the chord**using the following build. Draw a circle with center at point O and the chord CE, swipe the diameter through the centre and one of the points**of the chord**(C). It is known that any chord connects two points of the circle. Omit from the second point of intersection with the circle (E) to the center Of the radius EO. Thus, it is an isosceles triangle SEO with the base-chord CE. At a known angle at the base of the eco calculate the chord using the formula from the theorem on projections: CE = 2*a*cosUseful advice

If the chord passes through the center of a circle, it is diameter. The angle between intersecting chords corresponds to the sum of the measures of the arc, located in the corner, and arc in front of her. If the tangent to the circumference, and the chord form an angle, it is equal to the half-degree value of the arc subtended by the same chord.

# Advice 2 : How to calculate the chord of a circle

According to the definition of a curve in analytic geometry it represents a set of points. If any pair of such points to connect the cut, it can be called a chord. Outside of higher education institutions often consider the chord pertaining to the curve of the correct form, and in most cases this curve is a circle. To compute the length of chord connecting two points

**of a circle**, not very difficult.Instruction

1

If you draw two radii to the points

**of a circle**, the bounding**chord**, and the angle between them will be called "Central". At a certain value of this angle (θ) and the radius**of the circle**(R) length of the chord (d) determine, after considering the isosceles triangle formed by these three lines. Since the known angle is opposite the desired side (the base of the triangle), the formula must contain twice the product of the radius by the sine of half that angle: d = 2*R*sin(θ/2).2

Two points lying on a

**circle**together with a chord specify the boundary of some arc on the curve. Arc length (L) uniquely determines the value of the Central angle, so if it is given in terms of the problem along with the radius**of the circle**(R), to calculate the length of the chord (d) is also possible. The measure of the angle in radians expresses the ratio of arc length to radius L/R and in degrees, this formula should look like this: 180*L/(π*R). Substitute it into the equality of the previous step: d = 2*R*sin((180*L/(π*R))/2) = 2*R*sin(90*L/(π*R)).3

The size of the Central angle can be determined without the radius, if other than arc length (L) is known the total length

**of the circumference**(Lₒ) - it will be equal to the product of 360° to the length of the arc divided by the length**of a circle**: 360*L/Lₒ. And the radius can be expressed via the length**of the circumference**and the number PI: Lₒ/(2*π). Substitute all this into the formula from the first step: d = 2*Lₒ/(2*π)*sin((360*L/Lₒ)/2) = Lₒ/π*sin(180*L/ Lₒ).4

Knowledge of the square sector (S) carved in a circle two radii (R), held at the extreme point of the chord will also allow us to calculate the length of this chord (d). The size of the Central angle in this case can be defined as the ratio between twice the square and the squared radius: 2*S/R2. Substitute this expression in the same formula from the first step: d = 2*R*sin((2*S/R2)/2) = 2*R*sin(S/R2).