Two spherical balls lie on the ground touching ,if one ball has a radius of 8 units and the point - Maths - Areas Related to Circles

Question

Two spherical balls lie on the ground touching ,if one ball has
a radius of 8 units and the point of contact is 10 units above the
ground what is the radius of the other ball?

Ajanta Trivedi · Accepted Answer

let the radius of other circle be BO = x cm

AO = 8 cm. and the point of contact of two circles be O, such that OQ = 10 cm

triangle OPA and triangle BEA are similar triangles.

therefore

$\frac{O P}{A O} = \frac{B E}{A B} [B E = B D - E D = x - 8 a n d A B = A O + O B]$

therefore

$\frac{2}{8} = \frac{x - 8}{x + 8} [O P = O Q - P Q = 10 - 8 = 2] \frac{1}{4} = \frac{x - 8}{x + 8} x + 8 = 4 (x - 8) x + 8 = 4 x - 32 4 x - x = 32 + 8$

$3 x = 40 x = \frac{40}{3} c m$

thus the radius of the other circle is 40/3 cm.

hope this helps you.

cheers!!

Two spherical balls lie on the ground touching ,if one ball has a radius of 8 units and the point of contact is 10 units above the ground what is the radius of the other ball?