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 ⊙D2. A tangent of a circle is perpendicular to the radius at the point of tangency.3. BA−→is a secant of ⊙D4. If two parallel lines intersect a circle, the intercepted arcs between those lines are congruent.5. m∠ABF=mAB6. m∠ABE=12⋅mAH7. A secant is a line (segment, or ray) that intersects a circle in exactly one point.a 23467 b1237c 34567d 3e 1245f 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.

We have to find the statements that are true for the given figure.First, let us define-A tangent of…

Answered: Which of the following statements are…

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.

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