Locus of Midpoint of PAQ in Triangle Geometry

  • Thread starter Thread starter vaishakh
  • Start date Start date
  • Tags Tags
    Geometry Triangle
AI Thread Summary
The discussion focuses on finding the locus of the midpoint of line segment PAQ, where points P and Q lie on two intersecting circles at points A and B. A participant suggests that if C and D are the centers of the circles, the midpoint O of line segment CD can help determine the midpoint M of PAQ, particularly when OM is perpendicular to PAQ. They reference basic geometric properties learned in middle school but express difficulty in progressing further with the problem. The conversation seeks alternative methods or modifications to solve the locus challenge. The topic emphasizes the intersection of geometry and construction properties in triangle geometry.
vaishakh
Messages
334
Reaction score
0
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
 
Physics news on Phys.org
What have you tried?
 
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?
 
the title was given wrongly due to haste. i noted that after replying you
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Locus of all points -- Imprecise question?
Replies
12
Views
3K
Find locus of midpoint in circle intersections
Replies
2
Views
3K
Finding Area using parametric equation
Replies
12
Views
2K
Complex mapping z ↦ ω = (z − a)/(z − b)
Replies
5
Views
1K
Euclidean and non Euclidean geometries problems
Replies
4
Views
3K
Triangle inscribed in a circle
Replies
16
Views
3K
Triangle of centroids
Replies
5
Views
3K
What is the length of tangent AB in a geometry problem?
Replies
5
Views
2K
What is the geometric locus of triangle orthoprojections in alignment?
Replies
1
Views
2K
What is the reason behind alternate answers to a locus problem.
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top