Monday, July 20, 2009
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! :)
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
Example 2 & 3
**This videos is taken from ace-learning.org
Now, why not... TRY IT YOURSELF!
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°
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,
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:
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! :)
Friday, July 17, 2009
Here are some examples of how you can apply the property: Tangent from external point
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
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
Do go home and revise what you have learnt! :)
The end! Hope you have learnt how to use tangent perpendicular to radius property :)
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°
Done by: Ong Wan Ling
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
Friday, July 10, 2009
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Useful Linkstangent from external point
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