Question

The circumference 132cm of a circle Ais equal to the sum of the circumference of two circle B C the radius of the circle B is 14cm find the radius of the circle C

Answer 1

Step-by-step explanation:

Let the radii of circles B and C be $r_1</p><p>\: \& \:r_2\: cm\\</p><p>Given: r_1= 14\: cm$

Now it is given that:

C(circle A) = C( circle B) + C(circle C)

$\therefore \: 132 = 2 \pi \: r_1 + 2 \pi \: r_2 \\ \therefore \: 132 = 2( \pi \: r_1 + \pi \: r_2) \\ \therefore \: \frac{132}{2} = ( \pi \times 14+ \pi \: r_2 )\\ \therefore \: 66= \pi \times (14+ \: r_2) \\ \therefore \: 66= \frac{22}{7} \times (14+ \: r_2) \\ \therefore \: 66 \times \frac{7}{22} = 14+ \: r_2 \\ \therefore 3 \times 7 = 14 + r_2 \\ \therefore 21 = 14 + r_2 \\ \therefore 21 - 14 = r_2 \\ \therefore \huge \fbox{ r_2 = 7 \: cm}$

Thus the radius of circle B is 7 cm.