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Angle of intersection between two Circles Solution

STEP 0: Pre-Calculation Summary
Formula Used
angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between centers)^2))/(2*Radius 1*Radius 2))
∠A = arccos((((r1)^2)+((r2)^2)-((DBetweenCenters)^2))/(2*r1*r2))
This formula uses 2 Functions, 3 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
arccos - Inverse trigonometric cosine function, arccos(Number)
Variables Used
Radius 1 - Radius 1 is a radial line from the focus to any point of a curve. (Measured in Meter)
Radius 2 - Radius 2 is a radial line from the focus to any point of a curve. (Measured in Meter)
Distance between centers - Distance between centers is the distance between two centers of circle. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Radius 1: 11 Meter --> 11 Meter No Conversion Required
Radius 2: 13 Meter --> 13 Meter No Conversion Required
Distance between centers: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
∠A = arccos((((r1)^2)+((r2)^2)-((DBetweenCenters)^2))/(2*r1*r2)) --> arccos((((11)^2)+((13)^2)-((10)^2))/(2*11*13))
Evaluating ... ...
∠A = 0.844191681685787
STEP 3: Convert Result to Output's Unit
0.844191681685787 Radian -->48.3686204606561 Degree (Check conversion here)
FINAL ANSWER
48.3686204606561 Degree <-- Angle A
(Calculation completed in 00.016 seconds)

10+ Angle of Circle Calculators

Angle of intersection between two Circles
angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between centers)^2))/(2*Radius 1*Radius 2)) Go
Inscribed angle of Circle given radius and minor arc length
inscribed_angle = (90*Length of Minor Arc)/(pi*Radius) Go
Inscribed angle of Circle given radius and major arc length
inscribed_angle = (90*Length of Major Arc)/(pi*Radius) Go
Inscribed angle of Circle given other inscribed angle
inscribed_angle = (180*pi/180)-Inscribed angle 1 Go
Angle formed at centre of Circle given area of sector
central_angle = (Area of Sector*2)/(Radius^2) Go
Central angle of Circle given radius and major arc length
central_angle = Length of Major Arc/Radius Go
Central angle of Circle given radius and minor arc length
central_angle = Length of Minor Arc/Radius Go
Inscribed angle of Circle given central angle
inscribed_angle = Central Angle/2 Go
Angle formed at circumference of Circle given inscribed angle
angle_a = 2*Inscribed Angle Go
Angle subtended by arc of Circle given angle subtended on circumference
central_angle = 2*Angle A Go

Angle of intersection between two Circles Formula

angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between centers)^2))/(2*Radius 1*Radius 2))
∠A = arccos((((r1)^2)+((r2)^2)-((DBetweenCenters)^2))/(2*r1*r2))

What is a circle

A circle is a round shaped figure that has no corners or edges. The center of a circle is the center point in a circle from which all the distances to the points on the circle are equal. This distance is called the radius of the circle. Segment of a Circle, A segment is a region bounded by a chord of a circle and the intercepted arc of the circle. A segment with an intercepted arc less than a semicircle is called a minor segment. A sector with an intercepted arc greater than a semi-circle is called a major segment.

How to Calculate Angle of intersection between two Circles?

Angle of intersection between two Circles calculator uses angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between centers)^2))/(2*Radius 1*Radius 2)) to calculate the Angle A, The Angle of intersection between two circles formula is defined as the angle between their tangents at either of the intersection points. Angle A and is denoted by ∠A symbol.

How to calculate Angle of intersection between two Circles using this online calculator? To use this online calculator for Angle of intersection between two Circles, enter Radius 1 (r1), Radius 2 (r2) and Distance between centers (DBetweenCenters) and hit the calculate button. Here is how the Angle of intersection between two Circles calculation can be explained with given input values -> 48.36862 = arccos((((11)^2)+((13)^2)-((10)^2))/(2*11*13)).

FAQ

What is Angle of intersection between two Circles?
The Angle of intersection between two circles formula is defined as the angle between their tangents at either of the intersection points and is represented as ∠A = arccos((((r1)^2)+((r2)^2)-((DBetweenCenters)^2))/(2*r1*r2)) or angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between centers)^2))/(2*Radius 1*Radius 2)). Radius 1 is a radial line from the focus to any point of a curve, Radius 2 is a radial line from the focus to any point of a curve and Distance between centers is the distance between two centers of circle.
How to calculate Angle of intersection between two Circles?
The Angle of intersection between two circles formula is defined as the angle between their tangents at either of the intersection points is calculated using angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between centers)^2))/(2*Radius 1*Radius 2)). To calculate Angle of intersection between two Circles, you need Radius 1 (r1), Radius 2 (r2) and Distance between centers (DBetweenCenters). With our tool, you need to enter the respective value for Radius 1, Radius 2 and Distance between centers 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 Angle A?
In this formula, Angle A uses Radius 1, Radius 2 and Distance between centers. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • inscribed_angle = (90*Length of Minor Arc)/(pi*Radius)
  • inscribed_angle = (90*Length of Major Arc)/(pi*Radius)
  • central_angle = Length of Major Arc/Radius
  • central_angle = Length of Minor Arc/Radius
  • inscribed_angle = Central Angle/2
  • inscribed_angle = (180*pi/180)-Inscribed angle 1
  • central_angle = (Area of Sector*2)/(Radius^2)
  • central_angle = 2*Angle A
  • angle_a = 2*Inscribed Angle
  • angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between centers)^2))/(2*Radius 1*Radius 2))
Where is the Angle of intersection between two Circles calculator used?
Among many, Angle of intersection between two Circles calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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