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Let \(ABC\) be a triangle with \(\angle BAC=120^{\circ}\). Let \(D\) be the midpoint of \(BC\) and suppose that \(AD\) is perpendicular to \(AB\). Let \(E\) be the second point of intersection of the line \(AD\) with the circumcircle of triangle \(ABC\). Let \(F\) be the intersection of line \(AB\) and \(CE\).

(a) Prove that line \(DF\) is perpendicular to line \(BE\).

(b) Prove that \(DF = BC\).

Note by Sharky Kesa
1 year ago

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@Sharky Kesa : I am able to prove only the part (a). My proof is : It can be observed that D is the orthocentre of triangle BFE. Hence the result follows. Shrihari B · 11 months, 2 weeks ago

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I am solving thia Aditya Singh · 1 year ago

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@Aditya Singh Still solving? Sharky Kesa · 1 year ago

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