Meet the Inscribed Angle
Part of the Circles section of Coddy's Geometry journey. Lesson 26 of 62.
An inscribed angle has its vertex on the circle, and its arms are two chords. A central angle has its vertex at the center, and its arms are two radii. When both open onto the same arc, they are linked by one of the most useful facts about circles.
In the figure, ∠APB is inscribed, with P on the circle, and ∠AOB is central. Both stand on the arc AB at the bottom. Move P anywhere on the top part of the circle and something surprising happens: ∠APB does not change, and it is always exactly half of ∠AOB.
Challenge
Drag the point P around the top of the circle and watch ∠APB and ∠AOB. Then press Check.
Try it yourself
Drag the figure and watch
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Circles
1Parts of a Circle
Center and RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles