Problem Solving

You have to imagine that one circle is tangent to another circle from inside. So, in the circle with radii of 5 cm, draw the circle with radii 3 cm. Then, inside the circle with radii 3 cm, draw circle with radii 2 cm such that it touches only circle with radii of 3 cm and not the circle with radii 5 cm. In this configuration, you can get distance equal to 1 cm. It's a bit hard to explain without drawing. Hope you will get it. <i class="em em-smiley"></i>

BTGmoderatorDC wrote:Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle?

A) 0
B) 1
C) 3
D) 7
E) 13
Source: EMPOWERgmat

The correct answer is (B).



Regards,
Fabio.