Half the Central Angle
Part of the Circles section of Coddy's Geometry journey. Lesson 27 of 62.
The inscribed angle rule: an inscribed angle is half the central angle that stands on the same arc. Why? Draw the radius from P through O. It cuts the figure into two isosceles triangles, each made of two radii. In each one, the exterior angle at O is twice a base angle at P. Add the two halves and the whole central angle is twice the whole angle at P. When O lies outside the angle at P, the same two triangles give the rule by taking one half from the other instead of adding them.
Here the central angle AOB is 100°, so the inscribed angle APB on the same arc is 50°. Tap the inscribed angle and pick Inscribed angle.
Challenge
∠APB is inscribed in circle O and ∠AOB is the central angle on the same arc. Find ∠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