### Problem Statement:**Given:**- Circle $ O $ with radius $ OT = 17 $ and $ OX = 8 $.**Determine:**- The length of $ NT $.**Instructions:**- Use mathematics to explain how you determined the answer.### Diagram Explanation:The given image contains a diagram of a circle with the following labeled points and lines:- $ O $: Center of the circle.- $ T $: A point on the circumference such that the radius $ OT = 17 $.- $ X $: A point inside the circle such that $ OX = 8 $.- Line segments $ TN $ and $ PX $ intersect at point $ X $ within the circle.- $ P $ and $ N $ are other points of interest on the circle.### Steps to Determine $ NT $:1. **Understanding the Triangle:** - From the given information, $ OT $ is a radius of the circle, so $ OT = 17 $. - $ OX = 8 $, which is the distance from the circle’s center $ O $ to point $ X $ inside the circle.2. **Using the Pythagorean Theorem:** - Triangle $ OTX $ is a right-angled triangle since $ OT $ is the hypotenuse, $ OX $ a leg, and $ XT $ the other leg. - Applying the Pythagorean theorem: \[ OT^2 = OX^2 + XT^2 \] \[ 17^2 = 8^2 + XT^2 \] \[ 289 = 64 + XT^2 \] \[ XT^2 = 225 \] \[ XT = \sqrt{225} = 15 \]3. **Finding $ NT $:** - Notice that $ X $ lies between $ N $ and $ T $ on the circle’s diameter if extended. - Since the given problem usually applies the properties of secants and the intersecting chords in a circle, and $ XT $ being a leg of a right triangle, it is straightforward. - $ XT $ is partly the length from $ N $ to $ T $, so if

We know, A radius or diameter that is perpendicular to a chord divides the chord into two equal…

Answered: Given circle O where radius OT = 17 and…

Given circle O where radius OT = 17 and OX = 8. Determine the length of NT.Use mathematics to explain how you determined your answer. %3D P.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter44: Solution Of Equations By The Subtraction, Addition, And Division Principles Of Equality

Section: Chapter Questions

Problem 38A

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Question

### Problem Statement:

**Given:**
- Circle $ O $ with radius $ OT = 17 $ and $ OX = 8 $.

**Determine:**
- The length of $ NT $.

**Instructions:**
- Use mathematics to explain how you determined the answer.

### Diagram Explanation:

The given image contains a diagram of a circle with the following labeled points and lines:
- $ O $: Center of the circle.
- $ T $: A point on the circumference such that the radius $ OT = 17 $.
- $ X $: A point inside the circle such that $ OX = 8 $.
- Line segments $ TN $ and $ PX $ intersect at point $ X $ within the circle.
- $ P $ and $ N $ are other points of interest on the circle.

### Steps to Determine $ NT $:

1. **Understanding the Triangle:**
- From the given information, $ OT $ is a radius of the circle, so $ OT = 17 $.
- $ OX = 8 $, which is the distance from the circle’s center $ O $ to point $ X $ inside the circle.

2. **Using the Pythagorean Theorem:**
- Triangle $ OTX $ is a right-angled triangle since $ OT $ is the hypotenuse, $ OX $ a leg, and $ XT $ the other leg.
- Applying the Pythagorean theorem:
\[
OT^2 = OX^2 + XT^2
\]
\[
17^2 = 8^2 + XT^2
\]
\[
289 = 64 + XT^2
\]
\[
XT^2 = 225
\]
\[
XT = \sqrt{225} = 15
\]

3. **Finding $ NT $:**
- Notice that $ X $ lies between $ N $ and $ T $ on the circle’s diameter if extended.
- Since the given problem usually applies the properties of secants and the intersecting chords in a circle, and $ XT $ being a leg of a right triangle, it is straightforward.
- $ XT $ is partly the length from $ N $ to $ T $, so if

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