1. EXAMPLE 2 Use perpendicular bisectors SOLUTION STEP 1 Label the bushes A, B, and C, as shown. Draw segments AB and BC. 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? Gardening

2. EXAMPLE 2 Use perpendicular bisectors STEP 2 Draw the perpendicular bisectors of AB and BC By Theorem 10.4, these are diameters of the circle containing A, B, and C. 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.

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

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

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