Let $A, B, C$ and $D$ be four points in general position, and $\omega$ be a circle passing through $B$ and $C$. A point $P$ moves along $\omega$. Let $Q$ be the common point of circles $\odot (ABP)$ and $\odot (PCD)$ distinct from $P$. Find the locus of points $Q$.
Problem
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Tags: geometry
SHREYAS333
06.03.2019 15:53
I did by sine rule Edit:(Answer is Circle)
AlastorMoody
06.03.2019 16:14
Locus is a circle, just show that an $Q$ passes through two fixed points and the angle subtended by those fixed point with $Q$ is constant
MathBoy23
07.03.2019 05:06
Just as a side note. I guess it is important to say that the locus of $Q$ is a circle passing through $A$ and $D$ as they are fixed points throughout the problem.
ayan_mathematics_king
27.04.2019 15:33
Can anyone tell me the motivation behind thinking the locus of $Q$ as a circle?