Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is:

Solution (By Examveda Team)

Let smallest circle radius = R
Then biggest circle radius = (14 - R)

According to the question,
⇒ π(14 - R)²2 + πR² = 130π
⇒ (14 - R)² + R² = 130
⇒ 196 + R² - 28R + R² = 130
⇒ R = 3 cm
⇒ Radius of smallest circle
R = 3 cm