**Question:**

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

(a) 56 cm

(b) 42 cm

(c) 28 cm

(d) 16 cm

**Solution:**

(c) ∵ Circumference of first circle = 2 πr = πd1 = 36 π cm [given, d1 = 36 cm]

and circumference of second circle = πd2 = 20 π cm [given, d2 = 20 cm]

According to the given condition,

Circumference of circle = Circumference of first circle + Circumference of second circle

$\Rightarrow \quad \pi D=36 \pi+20 \pi \quad$ [where, $D$ is diameter of a circle]

$\Rightarrow \quad D=56 \mathrm{~cm}$

So. diameter of a circle is $56 \mathrm{~cm}$.

$\therefore \quad$ Required radius of circle $=\frac{56}{2}=28 \mathrm{~cm}$