in a traingle ABC, <BAC=80 and Q is the point on BC such that AQ bisects the angle BAC. There is also a point P on AB such that <QPC=40 and P is distinct from A. Prove that PQ=QC
any help would be awesome!!
thanx in advnace
in a traingle ABC, <BAC=80 and Q is the point on BC such that AQ bisects the angle BAC. There is also a point P on AB such that <QPC=40 and P is distinct from A. Prove that PQ=QC
any help would be awesome!!
thanx in advnace
We have $\displaystyle \widehat{QPC}=\widehat{QAC}$, then the quadrilater $\displaystyle ACQP$ can be inscribed in a circle.
Yields $\displaystyle \widehat{PAQ}=\widehat{PCQ}=\widehat{QPC}$, so the triangle $\displaystyle PQC$ is isosceles, then $\displaystyle PQ=QC$