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\(A,B,C\) are points on circle \(\omega\). Suppose points \(D,E\) are on \(AB\) and points \(F,G\) are on \(AC\) such that ...

\[\large \dfrac {b-c}{\sin (\frac {\angle B-\angle C}{2})}\]

In acute \(\triangle ABC\), the side lengths across from angles \(A,B,C\) are denoted \(a,b,c\) respectively. It ...

In triangle \(ABC\), \(O\) is the circumcenter and \(I\) is the incenter. \(P\) is a point on the exterior angle bisector of \(\Delta BAC\) such that \( PI \perp OI \). Extend ...

\(D\) lies on segment \(BC\), \(CE\) is tangent to circumcircle \(\odot ABD\) at \(E\), and \(\angle CAD=\angle BCE\).

If \(\frac {5}{3}BC=AC+AB\) and \(AC=33\). Find ...

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