Locus of Midpoint of PAQ in Triangle Geometry

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Homework Help Overview

The problem involves finding the locus of the midpoint of a line segment PAQ, where points P and Q lie on two intersecting circles at points A and B. The context is within triangle geometry.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use geometric properties related to the midpoints and perpendicularity but expresses difficulty in progressing further. Some participants inquire about the methods tried and suggest exploring modifications to the current approach.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the original poster's approach and questioning the assumptions made. There is no explicit consensus, but the dialogue appears to be productive in exploring different angles of the problem.

Contextual Notes

The original poster notes a potential error in the thread title, indicating a need for clarity in the problem statement. This may affect the interpretation of the problem.

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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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
 

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