In the given figure, two concentric circles with centre O are given. If the perpendicular from O is drawn on to AD. If AD = 20 cm and BC = 15 cm then find the value of AB.


 



We have OMAD.We know that  drawn from the centre of the circle to the chord bisects the chord.Since, AD is the chord of bigger circle and OMAD, thenAM = MD   = AD2 ....1Since, BC is the chord of smaller circle and OMBC, thenBM = MC  = BC2   .....2Now, AM = MD = AD2 = 202 = 10 cm       as, AD = 20 cmNow, BM = MC  = BC2 = 152 = 7.5 cm     As, BC = 15 cmNow, AB = AM - BM = 10 - 7.5 = 2.5 cm

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prove that the tangent at any point of a circle is perpendicular to the radius 
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Yes
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