Let ABCD be a square with side lengths 10 of units. Let CDE be a equilateral triangle so that E is outside the square. What is the radius of a circle passing through points A,B and E

2. Originally Posted by X1337
Let ABCD be a square with side lengths 10 of units. Let CDE be a equilateral triangle so that E is outside the square. What is the radius of a circle passing through points A,B and E
Hi

There may be a geometric solution but it can be solved by using coordinates (if you are allowed to).

Let O be the midpoint of [AB].
(OE) can be chosen as x-axis, and OB as y-axis.
Spoiler:

$R = \frac{5(10-3\sqrt{3})}{4}$

3. Originally Posted by X1337
Let ABCD be a square with side lengths 10 of units. Let CDE be a equilateral triangle so that E is outside the square. What is the radius of a circle passing through points A,B and E
Draw a picture. Add the diameter that passes through E and the mid points of CD and AB. Call the mid point of AB F

Now use the intersecting chord theorem to get AF.FB= (2r-EF)EF

You should be able to claculate EF from what is given and AF=FB=5.

CB