Here's my workings.

In Triangle ABD and Triangle ACE,

angle BAD = angle CAE (common)

angle ABD = angle ACE (exterior angle of cyclic quadrilateral)

angle ADB = angle AEC (sum of angles in triangle)

So, triangle ABD and triangle ACE are similar. (AAA similarity)

AB/AC = AD/AE

AB x AE = AC x AD

AB/AD = AC/AE

AB/AD = (AB+BC)/(AD+DE)

AB/AD = (AB+BC)/(AD+BC) - Since DE = BC

AB(AD + BC) = AD(AB + BC)

AB(BC) = AD(BC)

Therefore, AB = AD

I realized you didn't remove my ( )+... scribblings this time. Yay! It might be a bit strange, but it helps me when checking, and the other required conventional steps are there too.

]]>The wizardry in your factorization working is fine 😉 And for your info, this part actually carries 6 marks in the original question - so it's really open to debate on whether it's required to go beyond comparing the LHS & RHS (which, admittedly, is rather non-routine in an O-Level geometric proof question) just to obtain a final `AB`=`AD`, especially in exam conditions.

Actually The Temple has told its students that in an exam, the "best method" for each question shall be the one that enables you to "solve, convince yourself and show the examiner within the required time" i.e. one that acts as a cue to move on quickly to the next question.

Regarding you sis, Miss Loi knows who she is now - the cutie π ballerina with a thousand and one 多姿多采 activities. 😉

]]>I am a math lover also, but i never seen this tangent-secant being taught before both in sec school or university. Btw, i am an engineering graduate 😛

Kris

]]>My sister was the one who recently joined your sec4 class, because she was failing her a maths test! She called you herself, after I told her to, around the 1st week of March. From SMSS.

]]>*sneaks out and runs far far*

]]>**Who is your sister?!**

*extreme kaypoh mode ON & firing on all cylinders*

]]>He looked up, with tears streaming down his face ...

小妹 you win! Never in my years of selling tiger prawns have I met a 对手 as powerful as you and your friends.

But you watch out! My brothers and I will seek out a Mathematical Master and we shall meet again at this hawker centre in a year's time!

With that, the whole lot of them disappeared via 轻功 off the screen.

]]>