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Let ABC be a triangle with incentre I. I...

Let ABC be a triangle with incentre I. If P and Q are the feet of the perpendiculars from A to BI and CI, respectively, then prove that `(AP)/(BI) + (AQ)/(Cl) = cot.(A)/(2)`

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To prove that \(\frac{AP}{BI} + \frac{AQ}{CI} = \frac{\cot A}{2}\), we can follow these steps: ### Step 1: Understand the Geometry Let \(ABC\) be a triangle with incenter \(I\). Points \(P\) and \(Q\) are the feet of the perpendiculars from \(A\) to \(BI\) and \(CI\), respectively. ### Step 2: Use Triangle Properties In triangle \(APB\), since \(P\) is the foot of the perpendicular from \(A\) to \(BI\), we have: \[ ...
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