Complex Cyclic with Surprising Solution

Geometry Level 5

The circle \(S\) has the diameter \(AB\), which has an integer length. Points \(D\) and \(E\) are added on the circle to create the cyclic quadrilateral \(ADBE\), such that \(AD\), \(BD\), \(BE\) and \(AE\) have integer lengths and the lengths of \(AE\) and \(BD\) are prime numbers. What is:

\[ { (AD-5) }^{ 2 }+{ (BD-2) }^{ 2 }+{ (AE+2) }^{ 2 } \\ +{ (BE-1) }^{ 2 }-2(AB-3)(DE-3)-18\]

×

Problem Loading...

Note Loading...

Set Loading...