Enter the length of the minor arc and the radius of a circle into the calculator. The calculator will display the inscribed angle of that circle. View the image below to understand what the inscribed angle is.
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Inscribed Angle Formula
The following equation can be used to calculate the inscribed angle of a circle and minor arc.
A = [L/(2*pi*r)]*360/2
- Where A is the inscribed angle
- L is the length of the minor arc (arc length)
- r is the radius
In this equation, the section of [L/(2*pi*r)] * 360 is also known as the intercepted arc.
Inscribe Angle Definition
An inscribed angle is an angle contained within two arcs across a circle. The formula above uses the minor arc, or shortest arc, for the calculation of the inscribed angle.
Inscribed Angle Example
How to calculate an inscribed angle?
- First, determine the minor arc.
Measure the length of the minor arc.
- Next, determine the radius.
Measure the length of the radius.
- Finally, calculate the inscribed angle.
Using the formula above, calculate the inscribed angle.
Frequently Asked Questions (FAQ)
What is an inscribed angle in a circle?
An inscribed angle is formed when two chords of a circle intersect on the circle’s circumference. The vertex of the angle is on the circle, and its sides are defined by the two chords.
How do you calculate the length of a minor arc?
The length of a minor arc can be calculated using the formula (L = 2 pi r (theta / 360)), where (L) is the arc length, (r) is the radius of the circle, and (theta) is the central angle in degrees.
Can the inscribed angle formula be used for any type of arc?
Yes, the inscribed angle formula can be used for any arc, but it’s typically used for minor arcs because it directly relates the arc length to the inscribed angle. For major arcs, additional steps may be required.
Why is the inscribed angle formula important in geometry?
The inscribed angle formula is important because it provides a direct relationship between the arc length, the radius of a circle, and the inscribed angle. This relationship is crucial for solving various geometrical problems and proofs involving circles.
