The circumference of a circle is equal to the sum of the circumferences of two circles having diameters 36 cm and 20 cm. The radius of the new circle is

Let the bigger circle be C_{1} and other circles be C_{2} and C_{3}

Radius of circle C_{1} = r_{1}

Diameter of circle C_{2} = 36 cm

Radius of circle C_{2} = r_{2} = 36/2 cm = 18cm

Diameter of circle C_{3} = 20 cm

Radius of circle C_{3} = r_{3} = 20/2 cm = 10 cm

Circumference of circle C_{2} = 2πr_{2}

= 2 × π × 18 cm = 36π cm

Circumference of circle C_{3} = 2πr_{3}

= 2 × π × 10 cm = 20π cm

Circumference of circle C_{1} = Circumference of circle C_{2} + Circumference of circle C_{3}

⇒ 2πr_{1} = 2πr_{2} + 2πr_{3}

⇒ 2πr_{1} = 36π + 20π

⇒ 2πr_{1} = 56π

⇒ r_{1} = 28 cm

Radius of circle C_{1} = r_{1} = 28 cm

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