Question

Two circles touch externally. The sum of their areas is 130πsq. cm and the distance between their centres is 14 cm. Find the radii of the circles​

Answer 1

firstly area is measured in square.

diameter=14

radii = 14÷2

radii=7

Answer 2

$\underline\mathfrak\pink{Given:-}$

• Two circle touch externally. the sum of area 130π.
• The distance between their is 14cm.

$\large\underline\mathfrak{To \: find:-}$

• Find the radii of each circle ....?

$\large\underline\mathfrak\pink{Solutions:-}$

• Let radius of given circle be x cm and (14 - x) cm.

Sum of area of circle = [πx² - π(14 - x)²]

⟹ 130π = πx² + π(14 - x)²

⟹ 130π = π[x² + (14 - x)²]

⟹ 130 = x² + (14)² + x² - 2.x.14

⟹ 130 = 2x² + 196 - 28x

⟹ 2x² - 28x + 196 - 130 = 0

⟹ 2x² - 28x + 66 = 0

⟹ 2(x² - 14x + 33) = 0

⟹ x² - 14x + 33 = 0

⟹ x² - 11x - 3x + 33 = 0

⟹ x(x - 11) - 3(x - 11) = 0

⟹ (x - 11) (x - 3)

⟹ x = 11, 3

So, the radii of circle are 11cm and 3cm.

$\underline\mathfrak\pink{more \: \: important:-}$

• Circumference of circle = 2π = πD
• Area of circle = πr²
• Area of. semi-circle = 1/2πr²
• Perimeter of semi-circle = (πr + 2r)