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Which of the following statements are true? Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc. If a given statement does not contain names of geometrical objects, it is a general statement about circles and is not necessarily related to the diagram. 1.   CH−→  is a tangent of  ⊙D 2.   A tangent of a circle is perpendicular to the radius at the point of tangency. 3.   BA−→is a secant of  ⊙D 4.   If two parallel lines intersect a circle, the intercepted arcs between those lines are congruent. 5.   m∠ABF=mAB 6.   m∠ABE=12⋅mAH 7.   A secant is a line (segment, or ray) that intersects a circle in exactly one point. a 23467  b1237 c 34567 d 3 e 1245 f 2346

Which of the following statements are true? Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc. If a given statement does not contain names of geometrical objects, it is a general statement about circles and is not necessarily related to the diagram. 1.   CH−→  is a tangent of  ⊙D 2.   A tangent of a circle is perpendicular to the radius at the point of tangency. 3.   BA−→is a secant of  ⊙D 4.   If two parallel lines intersect a circle, the intercepted arcs between those lines are congruent. 5.   m∠ABF=mAB 6.   m∠ABE=12⋅mAH 7.   A secant is a line (segment, or ray) that intersects a circle in exactly one point. a 23467  b1237 c 34567 d 3 e 1245 f 2346

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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Which of the following statements are true?

Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc.

If a given statement does not contain names of geometrical objects, it is a general statement about circles and is not necessarily related to the diagram.

1.   CH−→  is a tangent of  ⊙D

2.   A tangent of a circle is perpendicular to the radius at the point of tangency.

3.   BA−→is a secant of  ⊙D

4.   If two parallel lines intersect a circle, the intercepted arcs between those lines are congruent.

5.   m∠ABF=mAB

6.   m∠ABE=12⋅mAH

7.   A secant is a line (segment, or ray) that intersects a circle in exactly one point.
a 23467


 b1237


c 34567


d 3


e 1245


f 2346
 
In the diagram presented, we observe a geometric construction involving a circle and several lines interacting with it. The circle is centered at point \( D \). Key elements of the diagram: - **Circle**: The circle is drawn with center \( D \). - **Points on the Circle**: - Points \( B \) and \( G \) lie on the circumference of the circle. - **Tangents and Extended Lines**: - Line \( AB \) and line \( BC \) are extended tangents to the circle, meeting at point \( B \). - Line \( EF \) is an extension that passes through point \( A \). - Line \( CG \) extends through point \( G \). - Line \( HE \) extends from point \( H \), meeting line \( FG \) at the extension. - **Chord and Secant Line**: - Line \( H \) lies on the circle, with \( DH \) and \( DG \) forming a chord intersecting the circle at point \( H \). This diagram can demonstrate properties of tangents, chords, and secants in a circle, helpful for understanding key concepts in geometry, such as the tangent-secant relationships and angle measures associated with these configurations.
Transcribed Image Text:In the diagram presented, we observe a geometric construction involving a circle and several lines interacting with it. The circle is centered at point \( D \). Key elements of the diagram: - **Circle**: The circle is drawn with center \( D \). - **Points on the Circle**: - Points \( B \) and \( G \) lie on the circumference of the circle. - **Tangents and Extended Lines**: - Line \( AB \) and line \( BC \) are extended tangents to the circle, meeting at point \( B \). - Line \( EF \) is an extension that passes through point \( A \). - Line \( CG \) extends through point \( G \). - Line \( HE \) extends from point \( H \), meeting line \( FG \) at the extension. - **Chord and Secant Line**: - Line \( H \) lies on the circle, with \( DH \) and \( DG \) forming a chord intersecting the circle at point \( H \). This diagram can demonstrate properties of tangents, chords, and secants in a circle, helpful for understanding key concepts in geometry, such as the tangent-secant relationships and angle measures associated with these configurations.
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