1. ## Circles problem

Three circles each with radius of 4, have centers A, E, and D, respectively. Two circles are tangent at E, and circles intersect at B (circle A and E) and C (Circle E and D). What is the perimeter of the quadrilateral ABCD (which seems to form a trapezoid).

I know the answer is 20 but I am having trouble proving that BC is 4 as well.

2. ## Re: Circles problem

Originally Posted by donnagirl
Three circles each with radius of 4, have centers A, E, and D, respectively. Two circles are tangent at E, and circles intersect at B (circle A and E) and C (Circle E and D). What is the perimeter of the quadrilateral ABCD (which seems to form a trapezoid).

I know the answer is 20 but I am having trouble proving that BC is 4 as well.
I have trouble picturing this, can you post a picture please?

3. ## Re: Circles problem

Originally Posted by donnagirl
Three circles each with radius of 4, have centers A, E, and D, respectively. Two circles are tangent at E, and circles intersect at B (circle A and E) and C (Circle E and D). What is the perimeter of the quadrilateral ABCD (which seems to form a trapezoid).

I know the answer is 20 but I am having trouble proving that BC is 4 as well.
You are dealing with 3 equilateral triangles.

BB'is the perpendicula bisector of AE; CC' is the perpendicular bisector of ED.

Therefore $BC = \frac12 AE + \frac12 ED$

Since |AE| = |ED| you'll get:

$BC = \frac12 AE + \frac12 ED = \frac12 AE + \frac12 AE = AE$