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EXAMPLE 2

Gardening. Three bushes are arranged in a garden as shown. Where should you place a sprinkler so that it is the same distance from each bush?. Label the bushes A , B , and C , as shown. Draw segments AB and BC. STEP 1. EXAMPLE 2. Use perpendicular bisectors. SOLUTION.

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EXAMPLE 2

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  1. Gardening Three bushes are arranged in a garden as shown. Where should you place a sprinkler so that it is the same distance from each bush? Label the bushes A, B, and C, as shown. Draw segments ABand BC. STEP 1 EXAMPLE 2 Use perpendicular bisectors SOLUTION

  2. Draw the perpendicular bisectors of ABand BCBy Theorem 10.4, these are diameters of the circle containing A, B, and C. STEP 2 STEP 3 Find the point where these bisectors intersect. This is the center of the circle through A, B, and C, and so it is equidistant from each point. EXAMPLE 2 Use perpendicular bisectors

  3. Use the diagram of Eto find the length of AC. Tell what theorem you use. Diameter BDis perpendicular to AC. So, by Theorem 10.5, BDbisects AC, and CF = AF. Therefore, AC = 2 AF =2(7) = 14. EXAMPLE 3 Use a diameter SOLUTION

  4. Find the measure of the indicated arc in the diagram. 3. CD From the diagram Diameter BDis perpendicular to CE. So, by Theorem 10.5, BDbisects CE, Therefore mCD=mDE. So mCD=9x° =72° for Examples 2 and 3 GUIDED PRACTICE SOLUTION So 9x°=(80 – x)° So 10x°=80° x=8°

  5. Find the measure of the indicated arc in the diagram. 4. DE mCD=mDE. So mDE=72° 5. CE mCE=mDE + mCD So mCE=72°+ 72° = 144° for Examples 2 and 3 GUIDED PRACTICE SOLUTION SOLUTION

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