9.4. Chords in Circles http://www.ck12.org
3.BD=12 andAC=3 in
⊙
A. Find the radius andmBD̂.Answers:
- The converse of Chord Theorem #2 would be: A diameter is also the perpendicular bisector of a chord. This is
not a true statement, see the counterexample to the right. - Because the distance from the center to the chords is congruent and perpendicular to the chords, then the chords
are equal.
6 x− 7 = 35
6 x= 42
x= 7- First find the radius. In the picture,ABis a radius, so we can use the right triangle 4 ABC, such thatABis the
hypotenuse. From Chord Theorem #3,BC=6.
32 + 62 =AB^2
9 + 36 =AB^2
AB=
√
45 = 3
√
5
In order to findmBD̂, we need the corresponding central angle,^6 BAD. We can find half of^6 BADbecause it is an
acute angle in 4 ABC. Then, multiply the measure by 2 formBD̂.