Leo is constructing a tangent line from point Q to circle P. What is his next step? **Constructing a Tangent Line from a Point**### Problem Statement:Leo is constructing a tangent line from point \(Q\) to circle \(P\). What is his next step?### Diagram:The diagram depicts a circle with center \(P\) and a point \(Q\) outside of the circle. A straight line segment \(PQ\) connects point \(P\) and point \(Q\).### Options for the Next Step:1. **Mark the point of intersection of circle \(P\) and segment \(PQ\).**2. **Construct arcs from point \(P\) that are greater than half the length of segment \(PQ\).** *(This option is selected)*3. **Construct a circle from point \(Q\) with the radius \(PQ\).**4. **Plot a new point \(R\) and create a line perpendicular to segment \(PQ\) from point \(R\).**### Explanation of the Selected Option:To construct a tangent line from point \(Q\) to circle \(P\), the next step mentioned in the problem is to "Construct arcs from point \(P\) that are greater than half the length of segment \(PQ\)."By choosing this option, Leo aims to identify the perpendicular bisector of the segment \(PQ\), which is instrumental in correctly placing the tangent point on the circle relative to point \(Q\).### Detailed Explanation:- **Mark the point of intersection of circle \(P\) and segment \(PQ\):** This step is incorrect because simply marking the intersection will not help in determining the tangent.- **Construct arcs from point \(P\) that are greater than half the length of segment \(PQ\):** This step is correct because drawing these arcs will help in finding the perpendicular bisector of \(PQ\). The perpendicular bisector will pass through the circle at right angles to segment \(PQ\) at the point where the tangent touches the circle.- **Construct a circle from point \(Q\) with the radius \(PQ\):** This step is incorrect because constructing such a circle does not aid in identifying the tangent line.- **Plot a new point \(R\) and create a line perpendicular to segment \(PQ\) from point \(R\):** This step is also incorrect as it does not directly help in defining the tangent line to circle \(P\).### Conclusion:Choosing the correct method to construct arcs

A tangent is a line that touches the curve at one point only.

Leo is constructing a tangent line from point Q to circle P. What is his next step? O Mark the point of intersection of circle P and segment PQ. Construct arcs from point P that are greater than half the length of segment PQ. O Construct a circle from point Q with the radius PQ. Plot a new point R and create and line perpendicular to segment PQ from point R.

Leo is constructing a tangent line from point Q to circle P. What is his next step? O Mark the point of intersection of circle P and segment PQ. Construct arcs from point P that are greater than half the length of segment PQ. O Construct a circle from point Q with the radius PQ. Plot a new point R and create and line perpendicular to segment PQ from point R.

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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Question

Leo is constructing a tangent line from point Q to circle P. What is his next step?

Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.

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