Constructing a similar triangle with a scale factor

Q.

$△ABC$ is a right angled triangle with $\angle ABC$ = 90${}^{\circ }$, AC = 13 cms and BC = 5 cm. BD is perpendicular to AC. If $△BDC$ ~ $△ABC$, find the length of BD.

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Q.

What will be the ratio of corresponding sides formed in the construction of a similar triangle to ΔABC, if C divides the line segment AB in the ratio 8:17?

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