276 



But 



Hence 

 Then 



PRACTICAL MATHEMATICS 



r 2 = <z 2 - (a - h) z 



= 7r(r 2 + h 2 ) 



146. T/ze Q/cZotd. 



Let a be the radius of the rolling circle. 

 Then OQ = arc PQ = a0 



If x, y are the co-ordinates of P, 

 Then x = OQ - PR 



= a0 a sin 



= (0 - sin 6) 



Also y = CQ - CR 



= a a cos 

 = a(l cos 0) 



The curve is evidently symmetrical about a vertical centre 

 line and for half the curve, the limits of are to n radians, 

 the limits of y are to 2a, and the limits of x are to Tia. 



Also 



dx 



dii 



-3! = a sin 



at) 



dy 



sin 



dx 1 cos 



