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Spot the Bow Tie

Part of the Circles section of Coddy's Geometry journey. Lesson 39 of 62.

When two chords cross inside a circle, the four points make a shape like a bow tie: the crossing chords are the knot, and the two outer sides close the wings. Look at any chord of the figure. The two corners on the same side of it both stand on it.

$Chords AC and BD crossing at E: angles 3 at B and 4 at C stand on the chord AD$

Here angle 3 at B and angle 4 at C both stand on the chord AD, and B and C are on the same side of it. So they are angles on the same arc, and equal. The angles at E are a different pair: there the chords cross, so those are vertical angles. A bow tie usually needs both rules.

Challenge

The chords AC and BD of circle O cross at E. Angles 1 and 2 are marked. Pick the rule that says they are equal, then press Check.

Try it yourself

$Name the rule that links them$

Name the rule that links them

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 Angle Using the Same ArcSpot the Bow TieSame 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