A pole has to be erected at a point on the boundary of a circular park ofdiameter 13 m in such a way that the difference of its distances from twodiametrically opposite fixed gates A and B on the boundary is 7 m. Is itpossible to do so ? If yes, at what distances from the two gates should thepole be erected ?

A pole has to be erected at a point on the boundary of a circular park

1.	A pole has to be erected at a point on the boundary of a circular park ofdiameter 13 m in such a way that the difference of its distances from twodiametrically opposite fixed gates A and B on the boundary is 7 m. Is itpossible to do so ? If yes, at what distances from the two gates should thepole be erected ?
Answer» Let P be the pole to be erected and A, B be the opposite fixed gates.Given, PA – PB = 7Let PA = a, PB = bHencea – b= 7⇒a= 7 +b...(1)In right ΔPAB,AB2= AP2+ BP2(By Pythagoras theorem)132= a2+ b2169 = (7 +b)2+ b2169 = 49 + 14b + 2b22b2+ 14b – 120 = 0b2+ 7b – 60 = 0b2+ 12b - 5b – 60 = 0b(b + 12) - 5(b + 12) = 0(b + 12)(b – 5) = 0Hence b = 5 or – 12But ‘b’ cannot be negativeTherefore, b = 5⇒a= 7 +5 = 12Hence, PA = 12 m and PB = 5 m