Chord Length of Circle given Perpendicular Length Calculator

✖Radius of Circle is the length of any line segment joining the center and any point on the Circle.ⓘ Radius of Circle [r]			+10% -10%
✖Perpendicular Length to Chord of Circle is the shortest distance from the center to the midpoint of a chord of a Circle.ⓘ Perpendicular Length to Chord of Circle [l_{Perpendicular}]			+10% -10%

✖Chord Length of Circle is the length of a line segment connecting any two points on the circumference of a Circle.ⓘ Chord Length of Circle given Perpendicular Length [l_c]

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Chord Length of Circle given Perpendicular Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Chord Length of Circle = 2*sqrt(Radius of Circle^2-Perpendicular Length to Chord of Circle^2)
l_c = 2*sqrt(r^2-l_{Perpendicular}^2)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Chord Length of Circle - (Measured in Meter) - Chord Length of Circle is the length of a line segment connecting any two points on the circumference of a Circle.
Radius of Circle - (Measured in Meter) - Radius of Circle is the length of any line segment joining the center and any point on the Circle.
Perpendicular Length to Chord of Circle - (Measured in Meter) - Perpendicular Length to Chord of Circle is the shortest distance from the center to the midpoint of a chord of a Circle.

STEP 1: Convert Input(s) to Base Unit

Radius of Circle: 5 Meter --> 5 Meter No Conversion Required
Perpendicular Length to Chord of Circle: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = 2*sqrt(r^2-l_{Perpendicular}^2) --> 2*sqrt(5^2-3^2)

Evaluating ... ...

l_c = 8

STEP 3: Convert Result to Output's Unit

8 Meter --> No Conversion Required

FINAL ANSWER

8 Meter <-- Chord Length of Circle

(Calculation completed in 00.004 seconds)

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< Chord Length of Circle Calculators

Chord Length of Circle given Perpendicular Length

LaTeX Go Chord Length of Circle = 2*sqrt(Radius of Circle^2-Perpendicular Length to Chord of Circle^2)

Chord Length of Circle given Diameter and Central Angle

LaTeX Go Chord Length of Circle = Diameter of Circle*sin(Central Angle of Circle/2)

Chord Length of Circle given Inscribed Angle

LaTeX Go Chord Length of Circle = 2*Radius of Circle*sin(Inscribed Angle of Circle)

Chord Length of Circle

LaTeX Go Chord Length of Circle = 2*Radius of Circle*sin(Central Angle of Circle/2)

Chord Length of Circle given Perpendicular Length Formula

LaTeX Go

Chord Length of Circle = 2*sqrt(Radius of Circle^2-Perpendicular Length to Chord of Circle^2)
l_c = 2*sqrt(r^2-l_{Perpendicular}^2)

What is a Circle?

A Circle is a basic two dimensional geometric shape which is defined as the collection of all points on a plane which are in a fixed distance from a fixed point. The fixed point is called the center of the Circle and the fixed distance is called the radius of the Circle. When two radii become collinear, that combined length is called the diameter of the Circle. That is, diameter is the length of the line segment inside the Circle which pass through the center and it will be two times the radius.

What are the properties of chords?

If the chords are parallel to each other, then the length of the arc between them will be the same. Chords of the same length are equidistant from the center of the circle. The greater the length of the chord, more closer to the center of the circle.

How to Calculate Chord Length of Circle given Perpendicular Length?

Chord Length of Circle given Perpendicular Length calculator uses Chord Length of Circle = 2*sqrt(Radius of Circle^2-Perpendicular Length to Chord of Circle^2) to calculate the Chord Length of Circle, Chord Length of Circle given Perpendicular Length formula is defined as the length of a line segment connecting any two points on the Circle and calculated using the perpendicular length from the center to the chord of the Circle. Chord Length of Circle is denoted by l_c symbol.

How to calculate Chord Length of Circle given Perpendicular Length using this online calculator? To use this online calculator for Chord Length of Circle given Perpendicular Length, enter Radius of Circle (r) & Perpendicular Length to Chord of Circle (l_{Perpendicular}) and hit the calculate button. Here is how the Chord Length of Circle given Perpendicular Length calculation can be explained with given input values -> 8 = 2*sqrt(5^2-3^2).

FAQ

What is Chord Length of Circle given Perpendicular Length?

Chord Length of Circle given Perpendicular Length formula is defined as the length of a line segment connecting any two points on the Circle and calculated using the perpendicular length from the center to the chord of the Circle and is represented as l_c = 2*sqrt(r^2-l_{Perpendicular}^2) or Chord Length of Circle = 2*sqrt(Radius of Circle^2-Perpendicular Length to Chord of Circle^2). Radius of Circle is the length of any line segment joining the center and any point on the Circle & Perpendicular Length to Chord of Circle is the shortest distance from the center to the midpoint of a chord of a Circle.

How to calculate Chord Length of Circle given Perpendicular Length?

Chord Length of Circle given Perpendicular Length formula is defined as the length of a line segment connecting any two points on the Circle and calculated using the perpendicular length from the center to the chord of the Circle is calculated using Chord Length of Circle = 2*sqrt(Radius of Circle^2-Perpendicular Length to Chord of Circle^2). To calculate Chord Length of Circle given Perpendicular Length, you need Radius of Circle (r) & Perpendicular Length to Chord of Circle (l_{Perpendicular}). With our tool, you need to enter the respective value for Radius of Circle & Perpendicular Length to Chord of Circle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Chord Length of Circle?

In this formula, Chord Length of Circle uses Radius of Circle & Perpendicular Length to Chord of Circle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Chord Length of Circle = 2*Radius of Circle*sin(Central Angle of Circle/2)
Chord Length of Circle = Diameter of Circle*sin(Central Angle of Circle/2)
Chord Length of Circle = 2*Radius of Circle*sin(Inscribed Angle of Circle)

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