a. If AB 5 5.3780 and AC 5 3.7820, find (1) DB and (2) ACB.(1) (2)b. If DB 5 3.0170 and ACB 5 7.3080, find (1) AB and (2) CB. (1) (2) ### Educational Exercise on Circle Geometry**Problem 20:**a. If $ AB = 5.378'' $ and $ AC = 3.782'' $, find (1) $ DB $ and (2) $ \angle ACB $.- (1) _______________- (2) _______________b. If $ DB = 3.017'' $ and $ \angle ACB = 7.308'' $, find (1) $ AB $ and (2) $ CB $.- (1) _______________- (2) _______________**Diagram Description:**The diagram on the right is a geometric representation of a circle with points $ A $, $ B $, $ C $, and $ D $ labeled on its circumference and interior. Point $ D $ is located on line segment $ AC $, forming a right triangle ($ \angle ADB $ is a right angle) within the circle. The circle's diameter is not provided, but intersects at points creating segments that are part of the problem. Points $ A $, $ B $, and $ C $ are marked on the circumference, and point $ D $ is marked inside the circle, indicating possible chord segments or angles for calculation.Note that the interior cross and arcs suggest usage of circle theorems or trigonometric identities to solve the problem, potentially involving properties of chords, secants, tangents, or inscribed angles.

Consider the given information and figure. AB=5.378'' and AC⏜=3.782'' In the given figure, the radius of the circle is perpendicular to chord and it divides the chord in to two equal parts. Thus, find the value of DB. AD=DB=AB2=5.3782=2.689And, in the given figure, the radius is perpendicular to chord. The length of AD is equal to length of DB. Thus, the arc cut by chord is divided in to equal part's. AC⏜= CB⏜= ACB⏜2 ACB⏜=2⋅AC⏜=2⋅3.7882''=7.564''(b) Consider the given values. DB=3.017'',ACB⏜=7.308'' Now, calculate same as the above part. AD=DB=AB2AB=2⋅DB=2⋅3.017''=6.034'' And, AC⏜= CB⏜= ACB⏜2=7.308''2=3.654''

Answered: 20. a. If AB = 5.378" and ÁC = 3.782",…

Math

Geometry

20. a. If AB = 5.378" and ÁC = 3.782", find (1) DB and (2) ACB. (1) (2) B b. If DB = 3.017" and ĀCB = 7.308", find (1) AB and (2) CB. (1) (2) A

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

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

a. If AB 5 5.3780 and AC 5 3.7820, find (1) DB and (2) ACB.

(1) (2)

b. If DB 5 3.0170 and ACB 5 7.3080, find (1) AB and (2) CB. (1) (2)

### Educational Exercise on Circle Geometry

**Problem 20:**

a. If $ AB = 5.378'' $ and $ AC = 3.782'' $, find (1) $ DB $ and (2) $ \angle ACB $.
- (1) _______________
- (2) _______________

b. If $ DB = 3.017'' $ and $ \angle ACB = 7.308'' $, find (1) $ AB $ and (2) $ CB $.
- (1) _______________
- (2) _______________

**Diagram Description:**

The diagram on the right is a geometric representation of a circle with points $ A $, $ B $, $ C $, and $ D $ labeled on its circumference and interior. Point $ D $ is located on line segment $ AC $, forming a right triangle ($ \angle ADB $ is a right angle) within the circle. The circle's diameter is not provided, but intersects at points creating segments that are part of the problem. Points $ A $, $ B $, and $ C $ are marked on the circumference, and point $ D $ is marked inside the circle, indicating possible chord segments or angles for calculation.

Note that the interior cross and arcs suggest usage of circle theorems or trigonometric identities to solve the problem, potentially involving properties of chords, secants, tangents, or inscribed angles.

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