Tangent Circles

Geometry Level 1

Three circles, with centers of $\Gamma_1$ , $\Gamma_2$ , $\Gamma_3$ , are externally tangential to each other. The radius of these circles are 10, 12 and 24 respectively, What is the perimeter of $\triangle\Gamma_1\Gamma_2\Gamma_3$ ?

The answer is 92.

3 solutions

Yan Yau Cheng
Apr 14, 2014

Since all 3 circles are tangent to each other, $\Gamma_1\Gamma_2 = 22$ , $\Gamma_1\Gamma_3 = 34$ , and $\Gamma_2\Gamma_3 = 36$ , Therefore the perimeter of $\triangle\Gamma_1\Gamma_1\Gamma_3$ is $22+34+36 = \boxed{92}$

Note that in conventional notation, $\Gamma_i$ is used to denote a circle, as opposed to a point (center of the circle).

Calvin Lin Staff - 7 years, 1 month ago

You will have to mention that the smaller circles are not included in the bigger circle

Harsh Depal - 7 years, 1 month ago

Ryan Redz
May 27, 2014

2*(10+12+24) = 92

Aliki Patsalidou
May 21, 2014

since all circles are tangent to each other the perimeter is equal=(12+10) + (12+24) + (24+10) =92

Tangent Circles

The answer is 92.

3 solutions

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