# 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 isA. 16 cmB. 28 cmC. 42 cmD. 56 cm

Let the bigger circle be C1 and other circles be C2 and C3

Radius of circle C1 = r1

Diameter of circle C2 = 36 cm

Radius of circle C2 = r2 = 36/2 cm = 18cm

Diameter of circle C3 = 20 cm

Radius of circle C3 = r3 = 20/2 cm = 10 cm

Circumference of circle C2 = 2πr2

= 2 × π × 18 cm = 36π cm

Circumference of circle C3 = 2πr3

= 2 × π × 10 cm = 20π cm

Circumference of circle C1 = Circumference of circle C2 + Circumference of circle C3

2πr1 = 2πr2 + 2πr3

2πr1 = 36π + 20π

2πr1 = 56π

r1 = 28 cm

Radius of circle C1 = r1 = 28 cm

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