# Thread: How long does it take you to solve this geometric puzzle?

1. Originally posted by ckiang

Don't quite understand, why "Add Point F on side AC such that angle FBC = 20°" ?

Where is the 20° derived from?

Regards
CK
to add a point F to make FBC an isosceles triangle... with point BCF=80, CFD will be 80 as well... so FBC is 20...

2. Originally posted by PsychoBoy

to add a point F to make FBC an isosceles triangle... with point BCF=80, CFD will be 80 as well... so FBC is 20...
I know, but how to derive this crucial first step? How does one know that an isoceles triangle is needed there in the first place?

Regards
CK

3. Originally posted by ckiang

I know, but how to derive this crucial first step? How does one know that an isoceles triangle is needed there in the first place?

Regards
CK
That's the whole trick. The triangle is ther but disguised. Once that line is drawn the solution becomes crystal clear.

4. Originally posted by roygoh

That's the whole trick. The triangle is ther but disguised. Once that line is drawn the solution becomes crystal clear.
I see. Any other solutions?

Regards
CK

5. how can that BFC be an isoceles triangle? Common sense that line BC is shorter than line BF. If you rotate line BC around point B, it's def shorter than line BF.

Even so, there is not geometric proof that BFC is isoceles. According to the solution, it's only an assumption. Can you prove that BFC ==FCB?

Like this the rest of your solution is wrong liao.

edited: ok.. I think it's quite easy to prove that BFC==FCB. whoever tot of that must be really smart.

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