**Problem Statement:**In circle $ O $, tangent $ \overline{MN} $ and secant $ \overline{MPQ} $ are drawn to the circle from exterior point $ M $. If $ MP = 6 $ and $ PQ = 8 $, then which of the following is the length of $ \overline{MN} $?Options:1. 72. 423. $ 4\sqrt{3} $4. $ 2\sqrt{21} $**Diagram Explanation:**The diagram accompanying the problem provides a visual representation:- There is a circle with center $ O $.- A tangent line $ \overline{MN} $ touches the circle at point $ N $ and extends to an exterior point $ M $ outside the circle.- A secant line $ \overline{MPQ} $ intersects the circle at two points $ P $ and $ Q $. The point $ M $ is outside the circle, and the line extends through the circle, forming segment $ MP $ and segment $ PQ $. Given:- $ MP = 6 $- $ PQ = 8 $We need to find the length of $ \overline{MN} $.

The secant of a circle is a line segment that cuts the circle at two points. The tangent line of a…

Answered: In circle O, tangent MN and secant MPQ…

In circle O, tangent MN and secant MPQ are drawn to the circle from exterior point M. If MP = 6 and PQ =8 then which of the following is the length of MN? N (1) 7 (2) 42 (3) 43 (4) 2/21

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Concept explainers

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

Question

**Problem Statement:**

In circle $ O $, tangent $ \overline{MN} $ and secant $ \overline{MPQ} $ are drawn to the circle from exterior point $ M $. If $ MP = 6 $ and $ PQ = 8 $, then which of the following is the length of $ \overline{MN} $?

Options:
1. 7
2. 42
3. $ 4\sqrt{3} $
4. $ 2\sqrt{21} $

**Diagram Explanation:**

The diagram accompanying the problem provides a visual representation:
- There is a circle with center $ O $.
- A tangent line $ \overline{MN} $ touches the circle at point $ N $ and extends to an exterior point $ M $ outside the circle.
- A secant line $ \overline{MPQ} $ intersects the circle at two points $ P $ and $ Q $. The point $ M $ is outside the circle, and the line extends through the circle, forming segment $ MP $ and segment $ PQ $.

Given:
- $ MP = 6 $
- $ PQ = 8 $

We need to find the length of $ \overline{MN} $.

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