The Right Angle Inside
Part of the Circles section of Coddy's Geometry journey. Lesson 33 of 62.
The angle in a semicircle is often the first step of a chase. Once you know the angle at P is 90°, the triangle APB has one known angle, and the triangle's angle sum does the rest.
Here AB is a diameter and the angle at A is 35°. The angle at P is 90°, so the angle at B is 180° - 90° - 35° = 55°. On the board: tap the angle at P, pick Angle in a semicircle, then tap the angle at B and pick Angles in a triangle. No right-angle square is drawn: the diameter is the reason.
Challenge
AB is a diameter of circle O and P is on the circle. Find ∠ABP, 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 Sectors7Angles in a Semicircle
Thales' TheoremThe Right Angle InsideIs That Enough?Semicircle With LettersRecap: Semicircles2Circumference
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