Question

18
(iv) Rs 1.056
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​

Answer 1

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

Learn More:

Find AD if AB ⊥ BC and DE ⊥ BC, AB=9 units , DE=3 units and AC=25 units

brainly.in/question/13533860

The perimeters of two similar triangles abc and pqr

brainly.in/question/7325454

In figure s and t are the points on the side PQ and PR

brainly.in/question/2596454