Two Radii, One Triangle
Part of the Circles section of Coddy's Geometry journey. Lesson 21 of 62.
Join two points of a circle that are not the ends of one diameter to each other and to the center, and you get a triangle with two radii for sides. Two radii are always equal, so the triangle is isosceles, even though no tick marks are drawn. The circle is the reason the sides are equal.
In the figure, OA and OB are radii, so triangle OAB is isosceles with its apex at the center O. Its base is the chord AB. The angles opposite the equal sides, at A and at B, are the base angles, and they are equal. That one fact powers most circle angle chases.
Challenge
A and B are points on circle O, joined to each other and to the center. Tap the two angles of triangle OAB that must be equal, then press Check.
Try it yourself
Find the right part on 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