Melody

Did you forget 0. ?  and what are the brackets for?

0.\overline{23}

\(0.\overline{23}\)

\(0.\overline{42}=\frac{42}{99}\)

you can finish it.

You found the wrong difference I think, but I really like your method for solving this.

It is so simple.

KKD can finish it himself, he is capable.  

Answered by Jugoslav.

Thanks Jugoslav:)

2*6*2*3

A guest impersonating a guest.   Is that your humor input?  Yes, it is mildly amusing.

But still no 'thank you'.

How many 3 digit numbers can be made using the digits in the list (1,2,3,3,3,9)?

333    one number

33(not3)   3*3=9 numbers

one or no threes  4P3 = 24 numbers

so that is    1+9+24 = 34 numbers

Maybe I misunderstood your delema?  It doesn't matter though.  Time to move on.  :)

oh yes there is a logical reason, . 

Any angle in a semicircle will be 90 degrees.  

This is an extension of the  theorem that: 

  Any angle on circumference subtended from an arc will always be half that as will be subtended to the centre.

(my wording may leave a little to be desired)

I knew AB was a diameter but I did not think to use the centre in my logic.