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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 9 Page 737

By Congruent Corresponding Chords Theorem in the same circle two minor arcs are congruent if and only if their corresponding chords are congruent.

127

Practice makes perfect

We want to find the value of x.

Let's recall the Congruent Corresponding Chords Theorem.

Congruent Corresponding Chords Theorem
In the same circle two minor arcs are congruent if and only if their corresponding chords are congruent.

We know that chords LM and PM are congruent. By the theorem the corresponding minor arcs are also congruent. mLM=mPM ⇕ mLM=x^(∘) By the Arc Addition Postulate and feature of the circle all central angles sum up to 360^(∘). 106^(∘)+x^(∘)+x^(∘)=360^(∘) Let's solve this equation for x.

106^(∘)+x^(∘)+x^(∘)=360^(∘)

▼

Solve for x

Add terms

106^(∘)+2x^(∘)=360^(∘)

LHS-106^(∘)=RHS-106^(∘)

2x^(∘)=254^(∘)

.LHS /2.=.RHS /2.

x^(∘)=127^(∘)

Subchapter links

Exercises p.736-740