In triangle \(ABD\), \(AD=17\text{ cm}\), \(AC=10\text{ cm}\), and \(\angle ABC=90^\circ\). Points \(D,C,B\) are collinear.
Given that \(\sin\angle ACD=\dfrac35\), find the exact value of
\(AB\),[1]
\tan\angle ACB\).[2]
Circle \(Q_1\) passes through \(A,B,C\), and circle \(Q_2\) passes through \(A,B,D\). Find the ratio of the circumference of \(Q_1\) to the circumference of \(Q_2\).[1]
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Answer:(a)(i) \(6\text{ cm}\) (ii) \(\frac34\) (b) \(10:17\)