Cyclic Meets Isosceles
Part of the Circles section of Coddy's Geometry journey. Lesson 56 of 62.
Tick marks and circles work together. A cyclic quadrilateral gives you opposite angles, and two equal sides give you an isosceles triangle. A diagonal joins the two.
Here ABCD is cyclic with AB = AD, and the angle at C is 80°. Opposite angles add to 180°, so the angle at A is 100°. The diagonal BD makes triangle ABD, which is isosceles with its apex at A, so its base angles are (180° - 100°) / 2 = 40° each.
Challenge
ABCD has all four corners on circle O, AB = AD, and the diagonal BD is drawn. Find ∠ABD, 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 Arc11Circle Chases
Tangent Meets ChordTwo Roads to One AngleEnough to Find It?Cyclic Meets IsoscelesRecap: Circle Chases3Area 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