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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 22 Page 738

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

8

Practice makes perfect

Let's look at the given diagram.

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 are given that AB≅ BC. According to the theorem, this must mean that DF and FE are equal. DF= FE ⇕ 3x-7= x+9 Let's solve the equation to find value of x.

3x-7=x+9

▼

Solve for x

SubEqn

LHS-x=RHS-x

2x-7=9

AddEqn

LHS+7=RHS+7

2x=16

DivEqn

.LHS /2.=.RHS /2.

x=8