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EXAMPLE 4 - PowerPoint PPT Presentation


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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.

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slide1

In the diagram, Nis the incenter of ABC. Find ND.

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

EXAMPLE 4

Use the concurrency of angle bisectors

SOLUTION

slide2

2

2

2

c =

a + b

400 =

2

NF + 256

2

144 =

NF

12 =

NF

2

2

2

20 =

NF + 16

EXAMPLE 4

Use the concurrency of angle bisectors

Pythagorean Theorem

Substitute known values.

Multiply.

Subtract 256 from each side.

Take the positive square root of each side.

Because NF = ND, ND = 12.

slide3

ANSWER

5

for Example 4

GUIDED PRACTICE

WHAT IF?

5.

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