Monday, July 20, 2009

ELLOS (:

Thanks for visiting our blog (:

Here in our blog,
you can learn 2 types of circle tangent property:
Tangent From External Point
and
Tangent Perpendicular Radius.

We hope through the videos,
examples and notes we provide can help you understand better ^^

Have fun learning!


we wrote @ 6:57 PM


Tangent From External Point

HELLOS (: In this post, we are going to teach you the property, Tangent From External Point of a Circle. There will videos and real life situations to associate you to learn better and know how to apply these properties accordingly. Feel free to browse through and comment in out tagbox! :)

You will be able to learn that:
a) tangents drawn to a circle from an external point are equal.
b) the tangents subtend equal angles at the centre.
c) the line joining the external point to the centre of the circle bisects the angle between the tangents.

The following video, taken from http://www.ace-learning.com.sg will let you have a better idea of what we are talking about, do enjoy! :)

video


we wrote @ 6:49 PM


Learn your Property Well!

A recap a little on what is tangent from external point:
a line which is from the meeting point between two tangents from the circle to the middle of the circle.


Now after looking at the explainations, let's move on to some examples :)
Please do try it out, so that you will learn the property even better through experiences! ;D




Simple Example





In the figure on the above, P is a point outside the circle, with centre O, PA and PB are two tangents drawn from P to touch the circle at A and B respectively. We can find that
i) AP = BP
ii) angle APO = angle BPO
iii) angle AOP = angle BOP

angle OAP = angle OBP = 90°
(tangent ⊥ radius - to know more, read the information from our previous posts.)
△AOP and △BOP are congruent (RHS Property)
AP = BP
angle APO = angle BPO and angle AOP = angle BOP


Credits to http://library.thinkquest.org/C0110248/geometry/circlete.htm



Example 2 & 3

video

**This videos is taken from ace-learning.org







Now, why not... TRY IT YOURSELF!

Question 1:






BC and CD are tangents to the following circle at B and D respectively. The centre of the circle is O. Given that angle BAD= 42° , find the obtuse angle of angle BCD.

Answer: 96°





Question 2:




It is given that YW and ZW are tangents to a circle at Y and Z respectively. The centre of the circle is O. If angle YXZ = 46°, find angle YWZ,



Answer: 88°



Questions are taken from ace-learning.org
**Answers are provided for you to check your answers.

Done By: Leona Ye

Once again, i would like to thank these websites:
http://library.thinkquest.org/C0110248/geometry/circlete.htm &
http://www.ace-learning.com.sg/sys/subjects/Qns.php
for providing us with the information we need in this post. Thank You! ;)

~By the way, please pardon us for the bad quality of the video and photos! :)



we wrote @ 5:07 PM


Friday, July 17, 2009

Real Life Situations

Have you wondered how to apply the properties you learn for circle?
Fret not.
Here are some examples of how you can apply the property: Tangent from external point
in real life situations.

Party hats:



As you can see, a circle shape (in white) can be drawn in the party hat. That makes the side of the hat (coloured in pink) touch the circle. This forms a tangent perpendicular to radius. *You will learn more about it in the following property* Since the tangents can be extended, there will be a point where the 2 tangents meet. Since the tangents have started out from the same point, the length of the tangents (from the point where they touch the circle to the point where the tangents meet) will be the same. That forms an isosceles triangle. If a line is drawn down from the tip of the and join to the radii of the circle as shown on the diagram, the 2 angles at the tip of the tangent (in white) will be the same.

Done By: Chen Liyun



we wrote @ 6:31 PM


Tangent perpendicular to radius

Hello! This post is done by all the group members: Leona, Liyun, Wanling and Jieyi :) Today we are going to teach you the property of the circle: Tangent Perpendicular to Radius.

The aims of this post is to learn:
1. what is a tangent
2. perpendicular
3. understand how the property and identiy it.


A tangent to a circle is perpendicular to the radius at the point of contact.
· A tangent intersects a circle at one point.
· Perpendicular means at right angles (meet at 90degrees).






Video of tangent perpendicular to radius

http://www.youtube.com/watch?v=E2uoEMwuyak






Video of tangent perpendicular to radius and tangents from external point
http://www.youtube.com/watch?v=bY3Jsi-tjrk






At the end of this, we have learnt that,
The line drawn perpendicular to the end point of a radius is a tangent to the circle.










Do go home and revise what you have learnt! :)



we wrote @ 5:03 PM




Learn your property well!

Now that you have understood the property, lets learn how to use the property: tangent perpendicular to radius to solve math problems. Remember that the tangent is perpendicular to the radius and the angle is 90degrees.
*Do try out the questions and check against the ans provided.
Here goes:


Example:

A point B is 17cm away from the centre O of the circle.AB is the tangent to the circle at A.Given that AB=15cm, find the radius of the circle.




OA is the radius.
angle OAB = 90° (tangent ⊥ radius)
(OA)square + (AB)square = (OB)square (By Pythagoras’ Theorem)
(OA)square + (15)square = (17)square
(OA)square = (17)square – (15)square
(OA)square = 64
OA = √64
OA = 8

TRY IT YOURSELF!
1) In the diagram WY is the tangent to the circle. O is the centre of the circle at X. Given that angle OYX= 46°, find angle OYX. Answer: 68°



2) PT is the tangent to the circle at A. The centre of the circle is 0. Given that angle TPO = 80°. Find angle CAP. Answer: 36°.

The end! Hope you have learnt how to use tangent perpendicular to radius property :)

Done by: Ong Wan Ling



we wrote @ 4:50 PM


Real Life applications
Bicycle

The bicycle wheel is a circle.The ground acts as a tangent to the circle and the radius of the wheel is perpendicular to the tangent.

Basketball
The basketball balances on the table at a point of contact at the circumference, with the ball's radius being perpendicular to the tangent, which is the table.

Do you know of any other real life examples we can use this property in? Do share it with us using our tagboard! :)

Post done by: JieYi :D



we wrote @ 4:23 PM


Friday, July 10, 2009

Test

ELEMENTARY MATHEMATICS PROJECT
1) attractive headings
2) all articles to be accompanied by graphics
3) every article have to have a first paragraph, summarising up that article.
4) graphics, games and/or cartoons to be related to mathematical topic that is discussed.
[optional to add in an article]
5) text are typed with font size 12 and double-spaced.
each article should be clearly distinguish from the others
6) each member has to do up at least one article by themselevs without any prompting from anyone.


we wrote @ 4:14 PM


About Us

Welcome to this page.
This page is created by
Leona, Li Yun, Wan Ling & Jie Yi,
students of
Nan Chiau High School,
class 3Crescendo
for a
elementary mathematics project.
Our Topic is on
the Properties of Circles.
[1) tangent perpendicular radius]
[2)tangent from external point]
Feel free to browse around and comment ^^

Useful Links

tangent from external point
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tangent perpendicular to radius
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Tagboard

Credits

LAYOUT by Juice

Information by:
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website 11
tangent perpendicular to radius
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