The Big Arc
Part of the Circles section of Coddy's Geometry journey. Lesson 29 of 62.
A chord that is not a diameter cuts a circle into two arcs, a small one and a big one. An inscribed angle stands on the arc on the far side of the chord from its vertex. When the vertex is on the small arc, the angle stands on the big arc, and its central angle is the reflex angle at O, the one bigger than 180°.
Here P is on the small arc between A and B. The marked central angle is 160°, but the angle APB opens the other way, onto the big arc. The reflex angle at O is 360° - 160° = 200°, so ∠APB is half of that, 100°. Two steps: Angles around a point for the reflex angle, then Inscribed angle.
Challenge
P is on the small arc between A and B of circle O. Find the inscribed angle ∠APB, then press Check.
Try it yourself
Find the marked part of the figure
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