Circle Geometry - Pretest

Today we did our pre test in class for Circle Geometry. More or less i think the whole class found that the long answer question and the last multiple choice question were the hardest, so i'll explain those. =)


LONG ANSWER
Determine the measure of ےECB, ےBDC, ےBAD, and ےDBE, where E is the centre of the circle.

So first of all we always start with a table that has STATEMENT on one side and REASON on the other.

It's obvious at this point that BE and CE are radii, therefor triangle BCE is an isosceles triangle. This also means that ےEBC and ے BCE are the same.

NOTE: CLICK ON BUBBLESHARE BOX TO SEE FULL EFFECTS. =)

We now know the exact amount of ےBCD and according to cyclic quadrilateral theorem ے BCD's and ےBAD's sum should equal 180°. So in order to find ےBAD, we subtract 30° and 40° from 180° and come up with 110°. Therefore ےBAD is 110°.


Another thing we looked at were the two triangles that are subtended by the same arc; triangle BCE and triangle BCD. Since all of us know of the central inscribed angle theorem ( AKA the star trek theorem ) we can easily point out that ےBDC is half the amount of ےBEC. As a result ےBDC = 100°/2 which equals 50°.


We only have one angle left! Angle DBE! So if we look closely at triangle BCD you'll realize that we only have one angle left to find, ےDBE. We also know that every the angles of a triangle sum up to be 180° and by subtracting every angle that we have we'll be able to come up with the value of ےDBE! :D

Which in this case in 20°! =)

Once you've found your information and proofs, your table (including "Statement" and "reason") should look something like this:



MULTIPLE CHOICE
In the diagram below, R, S, T, U are points on the circle with RS = RU = UT and SU = ST. Find the measure of ےUST.
a) 31°
b) 35°
c) 36°
d) 40°
e) none of these


The first thing you should always do is mark down what is given to you. Have a wishful thinking colour, a colour used for given facts and a colour used for things you have proven! ( it comes in handy :D )
I'll use purple as the facts that are given, blue for what we're looking for and orange for the facts i prove. =)

There's no particular order to do this in, but what i looked at first was the isosceles triangles. We can easily point out that ےRSU and ےRUS are the same and ےSUT = ےSTU.


Now if we look at RS, RU and UT they are all the same length. Which means that the angles subtended by this chord length will all be the same. SOOO.. ےRST = ےRUT = ےUST.


In order to find the exact degree that angle is we make three equations. (this is like going back to substitution in linear equations). Here are the three equations (let ےSRT = w):
1. w + z = 180
2. 3y + z = 180 --> z = 180 - 3y
3. w + 2y = 180 --> w = 180 - 2y

If we substitude 2 and 3 into 1, we can find out what Y is, which is ےUST.
180 - 2y + 180 - 3y = 180
180 + 180 - 180 = 2y + 3y
180 = 5y
36 = y

And there you have it!
c) 36° is the correct answer. =)


That's all for tonight! Sorry for the late entry, i had to go and watch my brother's christmas concert! haha. =) Well, no homework tonight, just study! Test tomorrow. Good luck guys!

HAPPY HOLIDAYS! =]




And the next scribe will bee..... -Zeph! Enjoy. =)

Blogging on blogging

Well the circle geometry was pretty fun till we had to start proving what was true, and that I think was the only thing in this unit that is still a little fuzzy. I tried my hardest on this unit but I really need to find a trick to memorize that darn theories. This unit I think was definitely one of the better ones, but good luck to all on the test.

B0B Natnael

Well, this unit as Cherieeee said was quite easy, and the thing that made it easy, i think, is that its pretty straight forward. I mean, right now we now whats on the test (at least the layout).

I think everyone will do very good on this test...and some excellent(its not u Lauressa..jk)

goodluck on the test everyone! ;D

BEEE - OHHH - BEEE (.. spells BOB)

Ahhhhhh! Another unit test!
Oh well, nothing to worry about. I honestly think that this unit, for me, was easier to understand than the ones we've had in the past. There's just something about circles, triangles and geometry that make them easy to learn. There were times when I hated this unit because of all the PROVING we needed to do. But I guess, the more proving we did in class, the easier it seemed, and my hatred lessened. Today we had the pretest in class, and I don't think I did my best. Although, I did put in my first effort, and got about 70% of the questions right! "Sweeeeeet!" Anyway, good luck to everyone on the test tomorrow!

-- Cherrrieeeee

Test Prep Exercises - Questions 1, 2 and 8

hey guys. Sandy and I had an agreement to switch days, if she chose me tomorrow.
So yes, its me EEDCE.



(1) In the diagram below, AB and CB are tangents to a circle with radius 10. If angle AB find x, the shortest distance from B to the circle.

cos50°=10/h
h = 10/cos50
h = 15.557units

x = h - 10
x = 15.557 - 10
x = 5.557 units

(2) Given: Circle with centre C
- Angle 1 = Angle 2
Prove AB=CD

statement proof
Angle 1 = Angle B given
BC ~= CD ~= AC radii
Triangle ABC is isoscles from above
Triangle ACD is isoscles from above

Therefore, AB cannot be congruent to CD.





8. Complete the proof:
Diagram clarification: E, D, C are collinear
Given: EA is tangent to the circle at A
AB EC

Statement Proof
AD // BC given
EA is tangent at A given

Angle 8 = Angle 7 Tangent-Chord Theorem
Angle 7 = Angle 5 Alternate Angles
Angle 6 = Angle 8 - Angle 9 Tangent-Chord Theorem
Angle 1 = Angle 2 Triangle ABC ~ Triangle AEC








Okay. thats it folks.
homework is to finish the rest of this pre-test if not yet done so.

SANDY will take it away tomorrow.

Circle geometry

Salutations fellow math students,

Today, for all you naughty kids that skipped (haha jk), we worked on five different circle problems that Mr. K had put up for the class to do. They were:

1) A chord that is 10cm long is 12 cm from the centre of a circle. Find the radius.












2) Line AB and line CD are two parallel chords in a circle. Line AB is 10cm and Line CD is 14 cm. Find the radius if the chords are 3cm apart.














3. a) O is the centre of each circle. Find the measures of the indicated angles. Justify your answer.


















3. b)

















4) Given:
-Line AC is tangent at B
- Angle 1 is congruent to angle 2

Prove: Line BD // Line FC



















So yeah that's what happened in class. Homework was posted up on the blog by our very own math teacher, Mr. K. And I choose........................................................................................SANDY cheeks to be our scribe for tomorrow's class.

BOB for the Circle Geometry Test

Hi everybody and in a few days it will be our circle geometry test and I'm almost ready. All I need to do is to study and get down all the stuff I miss about 2-3 weeks ago. I need to practice the recent work which is to prove somthing using the given info in a question which is not that bad but since it's new it doesnt hurt to do stuff. I need to get my theorems straight and finish the new review. That's all and good luck on the pre-test and test. =)