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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
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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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
Transcribed Image Text:**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
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