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A Panchayath has a circular park of diameter 13 metres (Figure 1). Panchayath committee
decided to renovate it. They erected a pole (P) on the boundary of a circular park in such
a way that the differences of its distances from two diametrically opposite fixed gates A
and B is 7 metres (Figure2).
B В
13
P
Figure 1
Figure 2
Observe figure 2 and answer the following
4
Answers
Given : A Panchayath has a circular park of diameter 13 metres . Erected a pole (P) on the boundary of a circular park in such a way that the differences of its distances from two diametrically opposite fixed gates A
and B is 7 metres
To Find : Distance of pole from A and B
Solution:
AB is diameter
AB = 13 m
Let say Distance from A = x and distance from B = x + 7
and point is C
as AB is Diameter hence ∠ACB = 90°
Hence ACB is right angled triangle
=> AC² + CB² = AB²
=> x² + (x + 7)² = 13²
=> x² + x² + 14x + 49 = 169
=> 2x² + 14x - 120 = 0
=> x² + 7x - 60 = 0
=> x² + 12x - 5x - 60 = 0
=> (x - 5)(x + 12) = 0
=> x= 5 or x = - 12
as distance can not be negative
Hence x = 5
x + 7 = 5 + 7 = 12
: Distance of pole from A and B are 5 and 12 m
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