Question

'O' is the centre of two concentric circles. In the bigger circle a longest chord AB= 17 cm is
taken and another chord BC = 8 cm is drawn such that BC is also a tangent to the smaller
circle at D, then AD =
(A) 241
(B) 20
(C) (117
(D) 257​

Answer 1

Answer:

In two concentric circle with centre 'O'.  

AD

 is the chord of the bigger circle.  

AD

 intersect the smaller circle at B and C.

Construction: Draw  

OE

 perpendicular to  

AD

 

Proof: AD is the chord of the bigger circle with centre 'O' and  

OE

 is perpendicular to  

AD

.

∵  

OE

 bisects  

AD

 (The perpendicular from the centre of a circle to a chord bisect it)

∴AE=ED     ....(i)

BC

 is the chord of the smaller circle with centre 'O' and  

OE

 is perpendicular to AD.

∵  

OE

 bisects  

BC

     (from the same theorem)

∴BE=CE    .... (ii)

Subtracting the equation (ii) from (i), we get

AE−BE=ED−EC

AB=CD

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Step-by-step explanation: