Circle Geo. Help Pls (1 Viewer)

[ttong]

Hey all, im still a noob at circle geo. and cant seem to get the following question and would really apperciate some assistance:

Find the length of the common chord of two intersecting circles whose radii are 15cm and 13cm and whose centres are 14cm apart.

Cheers

 

[ronnknee]

24 cm

There may be another easier method but this came up to my mind first

 

[peckerhead]

lets use the diagram above.

The 13, 14, 15 triangle has an area of 84. (Heron's rule*)

So the height (half of the common chord ) is 12.

Hence 24.




<?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:imagedata o:title="" src="file:///C:/DOCUME~1/chris/LOCALS~1/Temp/msoclip1/01/clip_image001.wmz">*A =Sqrt[s(s-a)(s-b)(s-c)] . a, b, c are the three sides and 's' is the semi perimeter.</v:imagedata>
<v:imagedata o:title="" src="file:///C:/DOCUME~1/chris/LOCALS~1/Temp/msoclip1/01/clip_image001.wmz">In this case P = 42 hence s=21</v:imagedata>
<v:imagedata o:title="" src="file:///C:/DOCUME~1/chris/LOCALS~1/Temp/msoclip1/01/clip_image001.wmz">A=sqrt[21*8*7*6)=84</v:imagedata>

 

[ttong]

Thanks a heap guys for your help, i really apprecitated it.

 

[ronnknee]

I don't think Heron's rule is in the syllabus
But nevertheless, it is still a quicker method of solving this question

 

[peckerhead]

Of course Heron's rule is not in the syllabus.

The syllabus is a statement of minimum requirement.

Good students will have no problem soaking up simple formulae such as this and using them to their advantage. This is where good teaching come to the fore. Teachers need to know far more than the syllabus and promote it where necessary. Kids will not be interested just for the sake of it, but if they can see is going to be beneficial to them they will lap it up.

Take this area of a triangle for example. I am aware of nine different ways to find the area. It all depends on the data one is given. When all we know is half base by height but we are given three sides it is a harder task to make the wrong formula work.

Here are a couple more I think any serious student should know:

* Area of a triangle given three coordinates on a number plane. This can be done very very easily with little effort. (this extends to any polygon)

* L'Hopital's rule for limits. This rule should handle any limits the HSC offers. One method for all limits. Surely that is an improvement.

* Area of a triangle again given the radius of the incircle and the perimeter.

Ask your teachers for more information on these and others.

Just to finish. One should note that competitions such as the westpac make use of these "unknown" formula and students will stuggle with them when really there is a straight forward answer with an established formula just waiting to be used. (eg try Ceva's theorem)
I will add here this may be the case in just one or two questions and the rest are very challenging

Ask your teachers for help. I am sure some are there who know these things and can point you in correct direction.

Peckerhead

Perhaps I should change my username