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Same Arc, Same Angle

Part of the Circles section of Coddy's Geometry journey. Lesson 37 of 62.

Draw a chord AB and pick two points P and Q on the circle, on the same side of the chord. The inscribed angles ∠APB and ∠AQB stand on the same arc. Each is half of the same central angle, so they are equal. This is the rule Angles on the same arc.

$Two inscribed angles of 41 degrees on the same arc AB$

In the figure, P and Q are both above the chord, so both angles are 41°. No central angle needs to be drawn: the rule works straight from one inscribed angle to the other. A point below the chord is different. Its angle opens onto the other arc, so it is not equal to these.

Challenge

Four points on circle O are joined to the ends of the chord AB. Tap every angle that must equal ∠1, then press Check.

Try it yourself

$Find the right part on the figure$

Find the right part on the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Circles

2Circumference

Around the Circle Using the Diameter Radius From Circumference Circumference With Letters 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 AngleUsing 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