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

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.

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.

GUIDED PRACTICE for Examples 2 and 3

3. CD

So 9x° = (80 – x)° So 10x° = 80° x = 8°

So mCD = 9x° = 72°

From the diagramDiameter 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

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

SOLUTION