Question

The sum of the areas of two circles which touch each other externally is 153?. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.​

Answer 1

Important steps to solve this question:

Let's say radius of the bigger circle is R and that of smaller circle is r. R+r=15 ⇒ R=15-r

Let's say radius of the bigger circle is R and that of smaller circle is r. R+r=15 ⇒ R=15-rThe sum of are of two circles = πR² + πr² = 153 π ⇒ π(R² + r²) = 153π

Let's say radius of the bigger circle is R and that of smaller circle is r. R+r=15 ⇒ R=15-rThe sum of are of two circles = πR² + πr² = 153 π ⇒ π(R² + r²) = 153πBy replacing R with r in the above equation, we get, r² - 15r + 36 = 0

Let's say radius of the bigger circle is R and that of smaller circle is r. R+r=15 ⇒ R=15-rThe sum of are of two circles = πR² + πr² = 153 π ⇒ π(R² + r²) = 153πBy replacing R with r in the above equation, we get, r² - 15r + 36 = 0On Solving we get r = 3 or 12.

Let's say radius of the bigger circle is R and that of smaller circle is r. R+r=15 ⇒ R=15-rThe sum of are of two circles = πR² + πr² = 153 π ⇒ π(R² + r²) = 153πBy replacing R with r in the above equation, we get, r² - 15r + 36 = 0On Solving we get r = 3 or 12.Hence, the ratio of the larger to the smaller radius = 12/3 = 4