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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 6 Page 737

In the same circle two chords are congruent if and only if they are equidistant from the center.

2

Practice makes perfect

In the given diagram, we see that the distance from the center to each chord is both 5 units.

Let's recall the Equidistant Chords Theorem.

Equidistant Chords Theorem
In the same circle two chords are congruent if and only if they are equidistant from the center.

We know that the chords GH and KL are equidistant from the center J. By the theorem they are therefore congruent, which means they have the same length. GH= KL ⇕ 9= 4x+1 Let's solve this equation for x.

9=4x+1

▼

Solve for x

SubEqn

LHS-1=RHS-1

8=4x

DivEqn

.LHS /4.=.RHS /4.

2=x

RearrangeEqn

Rearrange equation

x=2