If radii of the two concentric circles are 15cm and 17cm, then the length of each chord of one circle which is tangent to other is:   8cm       (b)   16cm   (c)  30cm    (d) 17cm

Explanation

`O` is the centre of both circles. Chord `A B` of larger circle touches smaller circle at P. Radius `O P perp` chord `A B`.


Radius `O A=15 cm` and radius `O P=15 cm`.


Applying Paythagoras theorem to `triangle A O P`,



`A P^{2}=O A^{2}-O P^{2}=17^{2}-15^{2}=289-225=64`



`Rightarrow {AP}=8`. Radius perpendicular to a chord bisects it so `{AP}=1 / 2 {AB}`



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