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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 23 Page 738

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

4

Practice makes perfect

Let's look at the given diagram. Notice that QS and RS have the same length which means these segments are congruent.

Let's recall Equidistant Chords Theorem.

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

Since the chords LM and PN are equidistant from the center S, they must be congruent according to the theorem. This means we can equate their lengths.

LM=PN

SubstituteII

LM= 16, PN= 4x

16= 4x

DivEqn

.LHS /4.=.RHS /4.

4=x

RearrangeEqn

Rearrange equation

x=4