It was noon at The Temple when Miss Loi was totally engrossed in trying to obtain the proof in a nasty Plane Geometry question sent earlier by a student.
After staring for what seemed like an eternity at the question’s diagram, her 阴阳眼 simply would not come and she was beginning to get very tired, partly due to the ridiculous phone call that cut short her sleep in the morning.
Never one to give up easily in the face of adversity and face the ignominy of hearing a “Haha! Miss Loi also dunno how to do!“, she rubbed her eyes and continued to stare intensely at the diagram.
So intense was her gaze that a circle in the diagram seemed to grow larger and larger as it beckoned her to lean closer and closer … so close that she felt almost at one with the question and could almost feel the closeness of the solution that she desperately sought.
Suddenly, an unknown force reached out and, to her horror, pulled her headfirst into the circle!
In the harrowing moments that followed, she was whisked through a tunnel lined with circles, triangles, tangents, secants, chords and all manner of grotesque polygons from the O-Level A-Maths Syllabus.
After what seemed like an eternity, she landed with a big thump right in front of a weathered-looking Right-Angled Triangle (RAT), who muttered
Oh boy here comes another 走火入魔 one.
Who are you? Where am I?
asked Miss Loi as she meticulously checked for any facial scar arising from the rough landing.
You’re at the Plane of Geometry. The realm of all killer Plane Geometry questions. And you, of all people, should know that I’m the Right-Angled Triangle alias Pythagoras Theorem – introduced to most during Sec One/Two and some say even PSLE! But they hardly think about me anymore.
Can you show me the way back to The Temple?
The RAT continued to grumble.
These days all the young people here only care about the ‘latest’ fads like the Tangent-Secant Theorem etc. They hardly think about me anymore.
Uncle! I really need your help! I’ve got a class to teach in a few hours’ time! AND I WANT MY NATIONAL DAY LONG WEEKEND!!!
I will show you the way if you can show me the following:
P is a point outside the circle such that PA and PB are tangents to the circle of centre O. M is the mid-point of AB and the secant line PDC cuts the chord AB at E.
Show that:
- ΔPMA is similar to ΔBMO
- PA×BM = BO×PM
- PE² = PD×PC − DE×CE
As Miss Loi has somehow lost her 阴阳眼 ability, can you help her find her way back to The Temple?
Meanwhile the RAT continued to mumble …
They hardly think about me anymore …
