CPhill

OK, Fiora........

OM^2 = PM^2 + OP^2 - 2(PM)(OP)sin 45

5  =  PM^2 + 8 - 2(PM)(2√2)(1/√2)

-3 = PM^2  - 4PM

PM^2 - 4PM + 3  = 0

(PM  - 1)(PM - 3)  = 0

PM = 1, 3

Is that correct ???

I see where I didn't take into account the SSA situation in my first answer!!!

Here's (1)

sin MPO/OM  = sin PMO/ PO

sin(45)/√5 = sin PMO /[2√2]   

1/[√2 * √5] = sin PMO /[2√2]

1/√5 = sin PMO / 2.......therefore

sin^-1( 2/√5) = PMO  = about 63.43°

Then angle MOP = [180 - 45 - 63.43]° = about 71.57º

So

√5/sin 45  = PM/sin71.57

PM = √5sin71.57 / sin45  =   3

$${\mathtt{1\,869\,000\,000\,000}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{112\,140\,000\,000\,000}}$$

We don't need to worry about the "1" out front acting as a multiplier since 1 times anything is just that thing.........so.....

√(1-(719.31/89602783250817600))  = .99999.......

Thanks, fiora....I totally mis-read that one.....!!!!

We can multiply the numerator and denominator by 40 and we have:

(-16)(15)/30          notice that (15)/(30) = 1/2...so we have

(-16) (1/2)  =

-8

Very nice, TR....!!!!

[ 3 + -2(3 + (-2)) - 3^2 ] /  [ -2 -3 + (-2)^2 ]  =

[3  -2(1) - 3^2] / [ -5 + 4]  =

[ 1  - 9] / [-1]  = 

[-8] / (- 1)   =   8/1   =   8

Here's one method.....but.....maybe not the fastest one !!!

Let the center of the circle lie at the origin and let both chords be parallel to the x axis.

The equation of the circle  is  x^2 + y^2   = 56.25

The chord of 12 cm in  length will have one of its endpoints at  (6,y₁)......and y₁ =

√[56.25 - 6^2] = √[56.25 -36 ]  = 4.5  { taking the positive value of the  root  }

And

The chord of 9 cm in  length will have one of its endpoints at  (4.5, y₂)......and y₂ =

√[56.25 - 4.5^2] = √[56.25 - 20.25 ]  = 6   {again, taking the positive value of the root}

So....the distance between the chords is  y₂ - y₁  = 6 - 4.5   = 1.5 cm

Here's a pic.....

Note that ED = 9, CB = 12 and  FG = 1.5