Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Let's analyze the situation step-by-step:
1. Understanding the Circle and Points:
- We have a circle [tex]\( \odot P \)[/tex] with center [tex]\( P \)[/tex] and radius [tex]\( 6 \)[/tex] mm.
- Point [tex]\( A \)[/tex] is given such that [tex]\( AP = 6 \)[/tex] mm. This implies point [tex]\( A \)[/tex] is on the circle since the distance [tex]\( AP \)[/tex] is exactly equal to the radius of the circle.
2. Determining the Positions of Points [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
- Point [tex]\( B \)[/tex] is given such that [tex]\( BP = 8 \)[/tex] mm.
- Since [tex]\( BP \)[/tex] is greater than the radius of the circle, point [tex]\( B \)[/tex] lies outside the circle.
3. Intersection Analysis Between Line Segment [tex]\( \overrightarrow{AB} \)[/tex] and the Circle [tex]\( \odot P \)[/tex]:
- Since point [tex]\( A \)[/tex] is on the circle and point [tex]\( B \)[/tex] is outside the circle, we need to evaluate how many points the line segment [tex]\( \overrightarrow{AB} \)[/tex] intersects the circle.
4. Checking Intersection Points:
- When one endpoint of the line segment (point [tex]\( A \)[/tex]) is on the circle and the other endpoint (point [tex]\( B \)[/tex]) is outside the circle, the line segment [tex]\( \overrightarrow{AB} \)[/tex] must intersect the circumference of the circle at two distinct points because it must enter and exit the circle.
- Hence, point [tex]\( A \)[/tex] provides one intersection point (since it lies on the circle), and the segment will re-enter the circle at another distinct point before reaching point [tex]\( B \)[/tex]. This confirms two intersection points overall.
### Conclusion
From the above analysis:
- The line segment [tex]\( \overrightarrow{AB} \)[/tex] intersects the circle [tex]\( \odot P \)[/tex] at exactly 2 points.
Thus, the correct answer is 2 points, and the best fitting answer from the given choices is:
A. 1 point or 2 points
Given the specific conditions, the answer more accurately aligns with this option as two points of intersection are consistent with such scenarios.
1. Understanding the Circle and Points:
- We have a circle [tex]\( \odot P \)[/tex] with center [tex]\( P \)[/tex] and radius [tex]\( 6 \)[/tex] mm.
- Point [tex]\( A \)[/tex] is given such that [tex]\( AP = 6 \)[/tex] mm. This implies point [tex]\( A \)[/tex] is on the circle since the distance [tex]\( AP \)[/tex] is exactly equal to the radius of the circle.
2. Determining the Positions of Points [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
- Point [tex]\( B \)[/tex] is given such that [tex]\( BP = 8 \)[/tex] mm.
- Since [tex]\( BP \)[/tex] is greater than the radius of the circle, point [tex]\( B \)[/tex] lies outside the circle.
3. Intersection Analysis Between Line Segment [tex]\( \overrightarrow{AB} \)[/tex] and the Circle [tex]\( \odot P \)[/tex]:
- Since point [tex]\( A \)[/tex] is on the circle and point [tex]\( B \)[/tex] is outside the circle, we need to evaluate how many points the line segment [tex]\( \overrightarrow{AB} \)[/tex] intersects the circle.
4. Checking Intersection Points:
- When one endpoint of the line segment (point [tex]\( A \)[/tex]) is on the circle and the other endpoint (point [tex]\( B \)[/tex]) is outside the circle, the line segment [tex]\( \overrightarrow{AB} \)[/tex] must intersect the circumference of the circle at two distinct points because it must enter and exit the circle.
- Hence, point [tex]\( A \)[/tex] provides one intersection point (since it lies on the circle), and the segment will re-enter the circle at another distinct point before reaching point [tex]\( B \)[/tex]. This confirms two intersection points overall.
### Conclusion
From the above analysis:
- The line segment [tex]\( \overrightarrow{AB} \)[/tex] intersects the circle [tex]\( \odot P \)[/tex] at exactly 2 points.
Thus, the correct answer is 2 points, and the best fitting answer from the given choices is:
A. 1 point or 2 points
Given the specific conditions, the answer more accurately aligns with this option as two points of intersection are consistent with such scenarios.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.