Find locus of midpoint in circle intersections

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In summary, the problem is asking for the locus (set of all possible points) of the midpoint of a line PAQ, where points P and Q lie on two intersecting circles and the midpoint must be equidistant from the centers of the circles. The conversation also suggests that the midpoint may lie at point A if OM (the midpoint of the line connecting the centers of the circles) is perpendicular to PAQ. However, the speaker is unable to solve the problem and asks for any other suggestions or modifications to their approach.
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vaishakh
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Two circles intersect at points A and B. PAQ is a straight line such that points P and Q lie on the two circles. Find the locus of the midpoint of PAQ
 
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Please, tell us what you have done so far in solving the problem. :)
 
  • #3
I have tride with saying that if c and d are the centres of the circle and o is its midpoint of CD then by structure as well as by sense we can feel that M is midpoint of PAQ where OA = OM. thus midpoint lies at A when OM is perpendicular to PAQ. these are basic construction properties which i have noted in middle school. but cannot proceed furhter. any other way or modification to this
 

1. What is the definition of a locus?

A locus is a set of points that satisfy a given condition or set of conditions. In other words, it is the path traced by a point or set of points that meet a specific criteria.

2. How do you find the locus of midpoint in circle intersections?

To find the locus of midpoint in circle intersections, you need to first draw the circles and determine their points of intersection. Next, find the midpoint of each of these points of intersection. Finally, the locus of midpoint in circle intersections is the line that connects all of these midpoints.

3. What is the significance of finding the locus of midpoint in circle intersections?

Finding the locus of midpoint in circle intersections can help solve problems in geometry and trigonometry. It can also be used to determine the center and radius of a circle, as well as to find the equation of a circle.

4. Can the locus of midpoint in circle intersections be a circle?

Yes, the locus of midpoint in circle intersections can be a circle if the two intersecting circles have the same radius.

5. Are there any real-world applications of finding the locus of midpoint in circle intersections?

Yes, there are many real-world applications of finding the locus of midpoint in circle intersections. For example, it can be used in navigation and mapping, as well as in designing roundabouts and circular structures in architecture and engineering.

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