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Is That Enough?

Part of the Circles section of Coddy's Geometry journey. Lesson 31 of 59.

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.

$Semicircle triangle with one angle of 62 degrees and one unknown$

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

$Is there enough information?$

Is there enough information?

All lessons in Circles

1Parts of a Circle

Center and Radius Chords and Diameters Recap: Parts of a Circle

4Arcs and Sectors

Arc Length Area of a Sector Find the Central Angle The Missing Central Angle Recap: Arcs and Sectors

7Angles in a Semicircle

Thales' Theorem The Right Angle InsideIs That Enough?Semicircle With Letters Recap: Semicircles

10Tangents

What a Tangent Is Tangent and Radius Tangent Lengths Two Tangents From a Point Tangents With Letters Recap: Tangents

2Circumference

The Hexagon Inside Around the Circle Radius From Circumference Recap: Circumference

5Radii Make Isosceles

Two Radii, One Triangle Base Angles From the Center The Angle at the Center Isosceles With Letters Recap: Radii and Triangles

8Angles on the Same Arc

Same Arc, Same Angle Using the Same Arc Spot the Bow Tie Same Arc With Letters Recap: Same Arc

11Circle Chases

Tangent Meets Chord Two Roads to One Angle Enough to Find It?Cyclic Meets Isosceles Recap: Circle Chases