CK-12 Geometry - Second Edition

9.3. Properties of Chords http://www.ck12.org

b) IfmBĈ= 80 ◦, findmCD̂.

Solution:

a) From the picture, we knowBD=CD. Because the chords are equal, the arcs are too.mCD̂= 125 ◦.

b) To findmCD̂, subtract 80◦from 360◦and divide by 2.mCD̂=^360
◦− 80 ◦
2 =

280 ◦

2 =^140

◦

Investigation 9-2: Perpendicular Bisector of a Chord

Tools Needed: paper, pencil, compass, ruler

1. Draw a circle. Label the centerA.


2. Draw a chord in

⊙

A. Label itBC.

3. Find the midpoint ofBCby using a ruler. Label itD.


4. ConnectAandDto form a diameter. How doesADrelate to the chord,BC?

Theorem 10-4:The perpendicular bisector of a chord is also a diameter.