In \(\triangle ABC\), \(AC=10\) cm, \(BC=8\) cm and \(AB=12\) cm. The perpendicular from \(C\) meets \(AB\) at \(N\). Let \(AN=a\), \(BN=b\), \(CN=h\).
Express \(a^2\) in terms of \(h\).
Express \(b^2\) in terms of \(h\).
Find \(a^2-b^2\).
Find \(a-b\).
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Answer:(i) \(100-h^2\); (ii) \(64-h^2\); (iii) \(36\); (iv) \(3\) cm.