HELLO ALL TIGERS how are you?
This is Robie here.

I just realised I'm addicted to everything.

• Tigers
• Chocolate
• Pewdiepie
• Pretty recently, Animal Jam. My user is darkestiger.
• One Republic (I'm addicted to this song lol)
• And pretty sadly I'm addicted to... math :(
• And I guess I like writing? I might post some stories I wrote...

So here's a "fun" math problem:

Two circles are externally tangent at point P. Segment CPD is parallel to common external tangent AB. Prove that the distance between the midpoints of AB and CD is AB. 

My terrible solution:

Call the radiuses x and y, with x the radius of the bigger circle.

oO = x+y      

(the distance between the centres of the circles)

Using the Pythagorean theorem, OE, IH and AB are sqrt(x^2-2xy+y^2+x^2+2xy+y^2) = sqrt(2x^2+2y^2).

HO = sqrt(x^2-y^2)

Now to find the distance between the midpoints...

BH = mP = x - HO = x-sqrt(x^2-y^2)     

(this is the length of the perpendicular)

I got to about there...

copy to view...

Diagram:

meh

goodbye paws