Inscribed Angle Calculator
Calculate inscribed and central angles using the inscribed angle theorem: Inscribed Angle = ½ × Central Angle.
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Frequently Asked Questions
What is an inscribed angle?
An inscribed angle is an angle formed by two chords that share an endpoint on the circle. The vertex of the angle is on the circle itself.
What is the inscribed angle theorem?
The inscribed angle theorem states that an inscribed angle is half the central angle that subtends the same arc. Formula: Inscribed angle = ½ × Central angle.
What is a central angle?
A central angle is an angle whose vertex is at the center of the circle. Its measure equals the arc measure it intercepts.
Why is the inscribed angle half the central angle?
This relationship comes from properties of isosceles triangles formed by radii. It's a fundamental theorem in circle geometry proven using triangle angle relationships.
What if the inscribed angle intercepts a semicircle?
An inscribed angle that intercepts a semicircle (180° arc) is always 90° (a right angle). This is called Thales' theorem.
Can different inscribed angles intercept the same arc?
Yes, all inscribed angles that intercept the same arc are equal. This is because they're all half of the same central angle.
What is arc measure?
The arc measure equals the central angle that intercepts it, measured in degrees. It's the "angular size" of the arc as seen from the center.
Where is the inscribed angle theorem used?
The inscribed angle theorem is used in geometry proofs, navigation, astronomy, optics, and anywhere circular arcs and angles are analyzed.