This theorem is famous for Math Olympians but never heard inside our classroom. I’m happy to share this to my readers for you to know this very interesting theorem.

Given a rectangle *ABCD*, we choose point P inside the rectangle and the distance from point A to P is a, B to P is b, C to P is c and D to P is d.

Then,

**Sample Problem:**

1. Let *ABCD* be a rectangle and let *P* be a point inside the rectangle. If *PA **= 8, PB=4* and *PD **= 7*, then what is the length of PC?

Solution:

*PA=a, PC=c, PB=b, PD=d*

Using the formula,

Therefore, PC=1.

2. ABCD is a rectangle and P is inside the rectangle. AP=x-1, BP=x+3, PC=x+2, PD=x-4. How long is BP?

Solution:

*PA=a, PC=c, PB=b, PD=d*

* *Using the formula,

*(x-1) ^{2}+(* x+2)

^{2}=( x+3)

^{2}+( x-4)

^{2}

Simplify and solve for x we have,

x=5

BP=x+2

=5+2

BP**=7**