Question

# Two unequal spherical balls lie on a field touching each other. The radius of the smaller ball is 9cm and the point of contact is 12cm above the field. Find the sum of the radii of the two balls.

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Solution

## Let radius of other circle be O1P=rOP=9cm & point of contact of two circles be P such that PR=12cm∴ △PQO∼△O1SO [By AA similarity]∴ PQOP=O1SOO1 [O1S=O1T−ST=r−9&OO1=OP+PO1]⇒12−99=r−9r+9⇒13=r−9r+9⇒r+9=3r−27⇒2r=36⇒r=18Sum of radii =9+18=27cm

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