If d1, d2(d2>d1) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, prove that d2^2 = d1^2 + c^2

Asked by Ritwika Sharma | 12th Mar, 2013, 08:53: PM

Expert Answer:

Answer: Given :  d1, d2 (d2>d1) be the diameters of two concentric circles and C be the lengths of a chord of a circle which is tangent to the other circle
To prove : d2= d1 2 + C2
 
Now
OQ = d2/2 , OR = d1/2 and PQ=c
Since PQ istangent to the circle 
therefore OR is perpendicular to PQ
=> QR = PQ/2 = c/2
 
Using pythagorus theorm in triangle OQR
OQ2 = OR2 + QR2
=> (d2 /2)2 = (d1/2)2 + (c/2)2
=>1/4 (d2)2 = 1/4 (d1)2 +(c)2
=> d22 = d12 +c2
Hence Proved

Answered by  | 12th Mar, 2013, 11:50: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.