**Geometry Problem:****Scenario:**In the figure below, line segment \( AB \) is tangent to circle \( O \) at point \( A \). Secant \( BD \) intersects circle \( O \) at points \( C \) and \( D \). The measure of arc \( AC \) is 70°, and the measure of arc \( CD \) is 110°. **Question:**What is the measure of angle \( ABC \)?**Diagram:**The figure consists of:- A circle with center \( O \).- A tangent line \( AB \) touching the circle at point \( A \).- A secant line \( BD \) intersecting the circle at points \( C \) and \( D \).- Arc \( AC \) is marked as 70°.- Arc \( CD \) is marked as 110°.**Options:**1. 40°2. 55°3. 70°4. 20°**Explanation:**To find the measure of angle \( ABC \), we utilize the following geometric property:- The angle formed between a tangent and a chord through the point of tangency is equal to half the measure of the intercepted arc. Therefore, \( \angle ABC = \frac{1}{2} \times \) (measure of arc \( AC \)).**Calculation:**Given that the measure of arc \( AC \) is 70°:- \( \angle ABC = \frac{1}{2} \times 70° = 35° \).However, considering both intercepted arcs:- Measure of arc \( AD \) = Measure of arc \( AC \) + Measure of arc \( CD \) = 70° + 110° = 180°.- \( \angle ABC = \frac{1}{2} \times \) (measure of arc \( AD \)) = \frac{1}{2} \times 180° = 90°.Thus:- Checking, since \( AB \) is a tangent and \( AD \) line spans directly across the circle:- The measure of angle \( ABC = 90°\).Therefore:- But usually here we see mistaken because only sum arcs inside:Measure arc add gives 180 total round can get missing part double counts check correct.And correct derivation show directly 20° = since angle interceptions both inside.Final Correct answer

Name: **Geometry Problem:****Scenario:**In the figure below, line segment \
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: **Geometry Problem:****Scenario:**In the figure below, line segment \( AB \) is tangent to circle \( O \) at point \( A \). Secant \( BD \) intersects circle \( O \) at points \( C \) and \( D \). The measure of arc \( AC \) is 70°, and the measure

Answered: Image /qna-images/answer/826cdc23-9954-4e23-8f16-69572e41b44a.jpg

Math

Geometry

In the figure below, line segment AB is tangent to circle O at point A, secant BD intersects circle O at points Cand D, the measure of arc AC = 70,and the measure of arc CD = 110.. What is the measure of angle ABC?

In the figure below, line segment AB is tangent to circle O at point A, secant BD intersects circle O at points Cand D, the measure of arc AC = 70,and the measure of arc CD = 110.. What is the measure of angle ABC?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section: Chapter Questions

Problem 2T

See similar textbooks

Similar questions

Draw an angle in standard position whose terminal side contains the point (2, â€“3). Find the distance from the origin to this point.
Object A is travelling along a circle of radius 2, and Object B is travelling along a circle of radius 5. The object have the same angular speed. Do the objects have the same linear speed? If not, which object has the greater linear speed?
Write a G-code program for the counterclockwise arc with starting point (-40, -20), ending point (30, -90), and center at (80, 30), where units are in millimeters.
Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of an isosceles triangle are joined by line segments.
Draw a triangle with three acute angles. Construct angle bisectors for each of the three angles. On the basis of the appearance of your construction, what seems to be true?
Find the exact distance between (5,3)and(2,8) . Find the coordinates of the midpoint of the line segment joining the two points.
A C Points A, B, and C lie on Circle O and ZABC and ZAỘC both intercept minor arc AC. Which of these best describes the relationship between mZABC and MZAOC? O MLABC > MZAOC O MLABC = 2mLAOC O MLABC = MZAOC O MLABC = }MLAOC
6. Triangle CDE with vertices C(-2,-2). D(1, -4), and E(-3, -4): a) dilation with scale factor of 4 centered (-1,-3) b) reflection in the line y = -x C' _ D' . E' - © Gina Wilson (All Things Algebra. LL county schoology.com/attachment/1788815912/docviewer
What is the center (in rectangular coordinates) of the circle r = -3 sin 0 ? (0.-3) 0, 3 ㅇ (0, v3) ㅇ(-금, )
You are sitting in a classroom next to the wall looking at the black- board at the front of the room. The blackboard is 12 ft long and starts 3 ft from the wall you are sitting next to. Show that your viewing angle is cot -1_X a = cot 15 if you are x ft from the front wall. 12' You 3' Wall Blackboard
11. Point B has coordinates (-12, 5) and lies on the circle whose equation is x² + y =169. If an angle is drawn in standard position with its terminal ray extending through point B, what is the cosine of the angle?
Triangle ABC is refilected across line m. Which statement(s) are true? B Select all that apply. O A'C' is perpendicular to C'B". mLA = mLA' O AB = A'B' CC' = BB'