O-Level Additional Math

[tutor4kids]

Hi, thank you for the solution.

Could you have me with the following question?

In the diagram below, ACB is a tangent to the circle at point C. This tangent is parallel to the line FE. Points F, G and H lie on the circle.
i) Prove that (EC)(CG) = (CF)^2.
ii) The line FE is extended to meet the circle at H. Prove (FE)(EH) = CF^2 - EC^2.

http://i52.tinypic.com/33zd7hv.jpg\">

Thank you.

[FrekiWang]

(i) (this is a very standard A Maths Question, Similarity is one of the standard approaches)

In FEC and GFC,
AngleEFC=AngleFCA=AngleFGC (hopefully you know why)
AngleFCE=AngeGCF
Thus FEC is similar to GFC
FE/GF=EC/FC=FC/GC
Cross-multiply 2nd and 3rd, we have EC x GC = FC^2(proven)

(ii) (usually (ii) is related to (i))
RHS=CF^2-EC^2
=EC x GC - EC^2 (from part (i))
=EC x (GC - EC)
=EC x GE
=FE x EH (intersecting chords thereom)
=LHS (proven)
Seriously, part(ii) is much easier. In the exam/test, if you cant prove part(i), you can always assume part(i) result and use it to prove part(ii)

[tutor4kids]

Hi,


Thank you very much for the prompt reply! I can understand the solution.
Thanks once again.

[FrekiWang]

tutor4kids:

Hi,


Thank you very much for the prompt reply! I can understand the solution.
Thanks once again.

Seriously, if you are a home tutor teaching A Maths, I would like to advise that you need more preparation for this topic. A lots of students are having problems in this topic so most likely they are going to ask a lot.

[tutor4kids]

Hi, thanks for the advice. I am not a home tutor for A Maths though, just seeking help on behalf of a friend. Anyway, thanks for your help.

[Herbie]

hi uncle tianzhu. Thanks very much.

[g131271]

Hi parents,


Does anyone of you can help me in this question? A million thanks to those who help to solve.

[b]A regular polygon has n sides. The size of each interior angle is 4 times the size of each exterior angle.
a. calculate the value of each exterior angle.
b. calculate the value of n.
c. hence find the sum of interior angles of polygon

[tianzhu]

Herbie:

hi uncle tianzhu. Thanks very much.

Hi

You're welcome.

Best wishes

[Herbie]

hi 131271,


A regular polygon has n sides. The size of each interior angle is 4 times the size of each exterior angle.
a. calculate the value of each exterior angle.
Exterior angle = 180/5 = 36 deg

b. calculate the value of n.
Each interior angle for a regular polygon=
144= {(n-2)x 180}/n
144n = (n-2) x180
180n-360= 144n
180n-144n=360
36n =360
n=10

c. hence find the sum of interior angles of polygon= 9x144 = 1296 deg

Hope it helps.

[Herbie]

hi i hv one qn which need help.


A lorry travels at 50km per hour. Given that diameter of itd wheel is 88Cm, find how many revolutions pwe minut the wheel is turning. Give yr answer to the nearest whole no.

Tq