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AB and AC are two chords of a circle of ...

AB and AC are two chords of a circle of radius r such that AB=2AC. If p and q are the distances of AB and AC from the centre Prove that `4q^(2)=p^(2)+3r^(2)`.

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To prove that \(4q^2 = p^2 + 3r^2\) given that \(AB = 2AC\) and \(p\) and \(q\) are the distances from the center \(O\) to the chords \(AB\) and \(AC\) respectively, we will follow these steps: ### Step 1: Draw the Circle and Chords 1. Draw a circle with center \(O\) and radius \(r\). 2. Draw two chords \(AB\) and \(AC\) such that \(AB = 2AC\). 3. Let \(AC = 2a\) (hence \(AB = 4a\)) for some length \(a\). 4. Let \(p\) be the distance from \(O\) to chord \(AB\) and \(q\) be the distance from \(O\) to chord \(AC\). ...
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