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Standard X
Mathematics
Pythagoras Theorem
A pole has to...
Question

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

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Solution



Let P be the pole to be erected and A, B be the opposite fixed gates.
Given, PA – PB = 7
Let PA = a, PB = b
Hence a – b = 7
⇒ a = 7 + b ..(1)

I n space r i g h t space capital delta P A B comma space A B squared space equals space A P squared space plus space B P squared space left parenthesis B y space P y t h a g o r a s space t h e o r e m right parenthesis space 13 squared space equals space a squared space plus space b squared space 169 space equals space left parenthesis 7 space plus space b right parenthesis squared space plus space b squared space 169 space equals space 49 space plus space 14 b space plus space 2 b squared 2 b squared space plus space 14 b space � space 120 space equals space 0 space b squared space plus space 7 b space � space 60 space equals space 0 space b squared space plus space 12 b space minus space 5 b space � space 60 space equals space 0 space b left parenthesis b space plus space 12 right parenthesis space minus space 5 left parenthesis b space plus space 12 right parenthesis space equals space 0 space left parenthesis b space plus space 12 right parenthesis left parenthesis b space � space 5 right parenthesis space equals space 0 space H e n c e space b space equals space 5 space o r space � space 12 space B u t space � b � space c a n n o t space b e space n e g a t i v e space T h e r e f o r e comma space b space equals space 5 space rightwards double arrow space a space equals space 7 space plus space 5 space equals space 12 space H e n c e comma space P A space equals space 12 space m space a n d space P B space equals space 5 space m

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