Question

Two farmers have circular plots. The plots are watered with the same water source placed in
the point common to both the plots as shown in the figure. The sum of their areas is 130π and
the distance between their centres is 14 m.Find the radii of the circles.What value is depicted
by the farmers?

Answer 1

Given :-

• Sum of areas of both circular plots = 130π .
• Distance between their centres = 14 m.

To Find :-

• Radii of the circles ?

Solution :-

Let us assume that, radius of bigger plot is R m and radius of smaller plot is r m.

so,

→ R + r = Distance between their centre = 14m. -------- Eqn.(1)

and,

→ πR² + πr² = 130π

→ π(R² + r²) = 130π

→ R² + r² = 130 ------------ Eqn.(2)

now, from Eqn.(1) ,

→ (R + r) = 14

squaring both sides,

→ R² + r² + 2Rr = 196

putting value of Eqn.(2),

→ 130 + 2Rr = 196

→ 2Rr = 196 - 130

→ 2Rr = 66

→ Rr = 33 ----------------- Eqn.(3)

now, we know that,

• (a - b)² = (a + b)² - 4ab.

so, using Eqn.(1) and Eqn.(3) now,

→ (R - r)² = (R+r)² - 4*R*r

→ (R - r)² = (14)² - 4*33

→ (R - r)² = 196 - 132

→ (R - r)² = 64

→ (R - r) = 8 .

adding the result in Eqn.(1) , we get,

→ (R + r) + (R - r) = 14 + 8

→ 2R = 22

→ R = 11 m.

therefore,

→ R + r = 14

→ 11 + r = 14

→ r = 14 - 11

→ r = 3 m.

therefore, the radii of the circles is 11m and 3m.

Learn more :-

PQ and XY are two chords of a circle such that PQ = 6 cm and XY = 12 cm and PQ||XY. If the distance between the chords i...

https://brainly.in/question/24793483

PQRS is a cyclic quadrilateral with PQ = 11 RS = 19. M and N are points on PQ and RS respectively such that PM = 6, SN =...

https://brainly.in/question/27593946