43 E. 45 11 D° s segment CE tangent to circle D? Why or why not? No; Pythagorean theorem does not hold true, so itť's not a right angle. Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem Yes, this looks like a right triangle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem. Yes; the Pythagorean Theorem holds true, so it is a aright angle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem. No; this doesn't look like a right triangle. Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem.
43 E. 45 11 D° s segment CE tangent to circle D? Why or why not? No; Pythagorean theorem does not hold true, so itť's not a right angle. Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem Yes, this looks like a right triangle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem. Yes; the Pythagorean Theorem holds true, so it is a aright angle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem. No; this doesn't look like a right triangle. Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem.
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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Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
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A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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![## Understanding Tangents and Right Triangles
### Figure Description:
The diagram includes a circle with center D and a triangle EDC. The sides of triangle EDC are labeled with lengths ED = 11, EC = 43, and DC = 45 units.
### Question:
Is segment CE tangent to circle D? Why or why not?
### Answer Options:
1. ○ No; Pythagorean theorem does not hold true, so it's not a right angle. Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem.
2. ○ Yes, this looks like a right triangle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem.
3. ○ Yes; the Pythagorean Theorem holds true, so it is a right angle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem.
4. ○ No; this doesn't look like a right triangle. Therefore, the segment is not tangent by the converse of the Perpendicular Tangent Theorem.
### Graph/Diagram Explanation:
The diagram represents a visual assessment where:
- The circle with the center at point D measures 11 units in radius (from D to E).
- Segment CE’s length is 43 units.
- Segment DC’s length is 45 units.
### Calculation using Pythagorean Theorem:
To determine if triangle EDC is a right triangle, apply the Pythagorean theorem:
\[
ED^2 + DC^2 = EC^2 \\
11^2 + 45^2 = 121 + 2025 = 2146 \\
43^2 = 1849
\]
### Conclusion:
Considering the calculations, 2146 does not equal 1849. Therefore, triangle EDC is not a right triangle according to the Pythagorean theorem.
### Correct Answer:
○ No; Pythagorean theorem does not hold true, so it is not a right angle. Therefore, the segment is not tangent by the converse of the Perpendicular Tangent Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb68be06-b69c-4f17-8aac-49ee20c407e4%2Fc33741b8-4006-4f97-a38c-c9fb4ab91d4e%2F7y1zwd7_processed.png&w=3840&q=75)
Transcribed Image Text:## Understanding Tangents and Right Triangles
### Figure Description:
The diagram includes a circle with center D and a triangle EDC. The sides of triangle EDC are labeled with lengths ED = 11, EC = 43, and DC = 45 units.
### Question:
Is segment CE tangent to circle D? Why or why not?
### Answer Options:
1. ○ No; Pythagorean theorem does not hold true, so it's not a right angle. Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem.
2. ○ Yes, this looks like a right triangle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem.
3. ○ Yes; the Pythagorean Theorem holds true, so it is a right angle. Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem.
4. ○ No; this doesn't look like a right triangle. Therefore, the segment is not tangent by the converse of the Perpendicular Tangent Theorem.
### Graph/Diagram Explanation:
The diagram represents a visual assessment where:
- The circle with the center at point D measures 11 units in radius (from D to E).
- Segment CE’s length is 43 units.
- Segment DC’s length is 45 units.
### Calculation using Pythagorean Theorem:
To determine if triangle EDC is a right triangle, apply the Pythagorean theorem:
\[
ED^2 + DC^2 = EC^2 \\
11^2 + 45^2 = 121 + 2025 = 2146 \\
43^2 = 1849
\]
### Conclusion:
Considering the calculations, 2146 does not equal 1849. Therefore, triangle EDC is not a right triangle according to the Pythagorean theorem.
### Correct Answer:
○ No; Pythagorean theorem does not hold true, so it is not a right angle. Therefore, the segment is not tangent by the converse of the Perpendicular Tangent Theorem.
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