Question

Two circles which are not congruent touch externally the sum of their areas is 130π sqcmannd the distance between their centres is 14 cm.find radii of circles

Answer 1

See the above attachment

Answer 2

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.

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