UPSKILL MATH PLUS

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Exercise condition:

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1. The perpendicular \(PS\) on the base \(QR\) of a \(\Delta PQR\) intersects \(QR\) at \(S\), such that \(QS\) \(=\) \(3\) \(SR\). Prove that \(2\) \(PQ^2 = 2PR^2 + QR^2\).
 
 
2. In the adjacent figure, \(ABC\) is a right-angled triangle with right angle at \(B\) and points \(D\), \(E\) trisect \(BC\). Prove that \(8AE^2\) \(=\) \(3AC^2 + 5AD^2\).
 
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3. \(P\) and \(Q\) are the mid-points of the sides \(CA\) and \(CB\) respectively of a \(\Delta ABC\), right angled at \(C\). Prove that \(4(AQ^2 + BP^2) = 5AB^2\).
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