A,P,Q lies on the Radical Axis
Posted: Sat May 15, 2021 12:36 pm
Hint Needed
Let \(ABC\) be a triangle and let \(D\) and \(E\) be points on the sides \(AB\) and \(AC\), respectively , such that \(DE\) is parallel to \(BC\). Let \(P\) be any point interior to triangle \(ADE\) , and let \(F\) and \(G\) be the intersections of \(DE\) with the lines \(BP\) and \(CP\), respectively. Let \(Q\) be the second intersection points of the circumcircles of triangles \(PDG\) and \(PFE\) . Prove that the points \(A, P, \text{and } Q\) are collinear .
Source
Let \(ABC\) be a triangle and let \(D\) and \(E\) be points on the sides \(AB\) and \(AC\), respectively , such that \(DE\) is parallel to \(BC\). Let \(P\) be any point interior to triangle \(ADE\) , and let \(F\) and \(G\) be the intersections of \(DE\) with the lines \(BP\) and \(CP\), respectively. Let \(Q\) be the second intersection points of the circumcircles of triangles \(PDG\) and \(PFE\) . Prove that the points \(A, P, \text{and } Q\) are collinear .
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