Three circles with radii of 2 cm, 3 cm and 5 cm, respective

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Dec 22, 2018 5:37 am

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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

OA B

Source: EMPOWERgmat

Source: Beat The GMAT — Problem Solving | Sat Dec 22, 2018 5:37 am

himalaya savalia: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sat Dec 22, 2018 11:25 am

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by himalaya savalia » Sat Dec 22, 2018 11:55 am

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>

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sun Dec 23, 2018 5:13 pm

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.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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