Final: Deep in the Circle
Part of the Circles section of Coddy's Geometry journey. Lesson 61 of 62.
A, B, C and D lie on a circle with center O, in that order, and the side DC is extended past C to F. The angle between CB and CF is 68°. The radii OB and OD and the chord BD are drawn. Find ∠OBD.
Challenge
A, B, C, D are on circle O, DC is extended to F, and the radii OB, OD and the chord BD are drawn. Find ∠OBD, 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 Angles9Cyclic Quadrilaterals
Four Corners on a CircleOpposite Angles Add to 180Is It Cyclic?Cyclic With LettersRecap: Cyclic Quadrilaterals12Final Challenges
Final: The Pizza SliceFinal: Paths to the PondFinal: The Curved TrackFinal: Deep in the CircleFinal: Angle Into Arc