Is That Enough?
Part of the Circles section of Coddy's Geometry journey. Lesson 34 of 62.
The angle in a semicircle gives you 90° for free, but only 90°. The other two angles of the triangle share the remaining 90° between them, and nothing about the circle says how. You need one more measure to split it.
Here the angle at B is 62°, so there is enough: the angle at P is 90° and the angle at A is 180° - 90° - 62° = 28°. Take the 62° away and the angle at A could be anything from just above 0° to just below 90°, depending on where P is. That is the question to ask before any chase: does the figure fix this value?
In this task you answer Yes or No.
Challenge
AB is a diameter of circle O and P is on the circle. Is there enough information to find ∠PAB? Answer, then press Check.
Try it yourself
Is there enough information?
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