EXAMPLE 4

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EXAMPLE 4 Use the concurrency of angle bisectors the diagram, N is the incenter of ABC. Find ND. SOLUTION By the Concurrency of Angle Bisectors of a Triangle Theorem, the incenter N is equidistant from the sides of ABC. So, to find ND, you can find NF in NAF. Use the Pythagorean Theorem stated on page 18.

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In the diagram, N is the incenter of ABC . Find ND. By the Concurrency of Angle Bisectors of a Triangle Theorem, the incenter N is equidistant from the sides of ABC . So, to find ND , you can find NF in NAF . Use the Pythagorean Theorem stated on page 18. EXAMPLE 4. - PowerPoint PPT Presentation

Transcript of EXAMPLE 4

Page 1: EXAMPLE 4

EXAMPLE 4 Use the concurrency of angle bisectors

In the diagram, N is the incenter of ABC. Find ND.

SOLUTION

By the Concurrency of Angle Bisectors of a Triangle Theorem, the incenter N is equidistant from the sides of ABC. So, to find ND, you can find NF in NAF. Use the Pythagorean Theorem stated on page 18.

Page 2: EXAMPLE 4

EXAMPLE 4 Use the concurrency of angle bisectors

c =2 a + b2 2 Pythagorean Theorem

NF + 1622

20 =2

Substitute known values.

400 = NF + 2562

Multiply.

144 = NF 2

12 = NF

Subtract 256 from each side.

Take the positive square root of each side.

Because NF = ND, ND = 12.

Page 3: EXAMPLE 4

GUIDED PRACTICE for Example 4

5. WHAT IF?

In Example 4, suppose you are not given AF or AN, but you are given that BF = 12 and BN = 13. Find ND.

5ANSWER


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