One medium circle and one small circle touch each other, and each circle touches the larger circle.
which is the area of the shaded region?
a.72 π square centimeters
b. 97 π square centimeters
c. 26 π square centimeters
d. 169 π square centimeters

The area of shaded is 72π cm² ⇒ answer A

Step-by-step explanation:

* Lets explain how to solve the problem

- The area of any circle is A = πr², where r is the radius of the circle

- The length of the radius of a circle is 1/2 the length of its diameter

- From the figure:

∵ There are two inscribed circles touch the larger circle internally

  and touch each other externally

∴ The centers of the three circles are collinear

∴ The diameter of the larger circle = the sum of the diameters of

   the two inscribed circles

∵ The radii of the inscribed circles are 4 cm and 9 cm

∵ The diameter = twice the radius

∴ The diameters of the inscribed circles are 2 × 4 = 8 cm and

  2 × 9 = 18 cm

∴ The diameter of the larger circle = 8 + 18 = 26 cm

∵ The radius of the circle = 1/2 diameter

∴ The radius of the larger circle = 1/2 × 26 = 13 cm

- The area of the shaded part is the difference between the

  area of the larger circle and the sum of the areas of the two

  inscribed circles

∵ A = πr²

∴ The area of the larger circle = π(13)² = 169π

∵ The sum of areas of the inscribed circles = π(4)² + π(9)²

∴ The sum of areas of 2 circles =16π + 81π = 97π

∵ Area of shaded = A larger circle - sum of A of 2 circles

∴ Area of shaded = 169π - 97π = 72π

* The area of shaded is 72π cm²

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step-by-step explanation: