Okay, with the #MathsEd crowd here, let's do some Sunday night #mathscpd !

I teach IGCSE and so teach the intersecting chords theorem. This says that if chords $AB$ and $CD$ intersect at a point $P$ (possibly outside the circle) then $AP\times PB=CP\times PD$. Often, the lengths are given in such a way that we set up a quadratic. For example, if $x=AP$ and $AB=9$ we could end up with $x(9-x)=18$.

Conventional techniques then say to expand this to a quadratic, which would be $x^2-9x+18=0$, and then factorising and solving it, which involves finding two numbers that add to $-9$ and multiply to $18$.

But that's exactly what the equation $x(9-x)=18$ describes! So why bother multiplying out and rearranging in the first place?

Maybe a better approach would be to view $x(9-x)=18$ as the canonical form in the first place!

Well, I’m not sure about being an #edutooter yet, but here goes… I will miss my Twitter Maths community if it all goes up in but really hope I can find you all again here! #introduction #maths #mathscpd #mathscpdchat #mathstlp