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#1 2013-08-09 10:36:34

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

some problems

Sector OAB is a quarter of a circle of radius 3. A circle is drawn inside this sector, tangent at three points as shown. What is the radius of the inscribed circle? Express your answer in simplest radical form.


I see you have graph paper.
You must be plotting something
lol

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#2 2013-08-10 00:36:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: some problems

Hi;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2013-08-10 01:14:15

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: some problems

hi

The sector is ABC with centre B

The smaller circle has centre O with tangent points at  D, E and F as shown in the diagram.

For tangents at D and F, the angles at D and F will be 90, so ODBF is a square.

Let radius OD be r.

Use pythag to calculate OB.

Add EO ( = r ) and this is EB ( = 3 )

Hence find r.

Bob

View Image: cooljackiec13.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2013-08-12 14:57:42

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: some problems

these are all so hard sad

View Image: ScreenHunter_281 Aug. 12 19.55.jpg View Image: ScreenHunter_282 Aug. 12 19.55.jpg View Image: ScreenHunter_283 Aug. 12 19.55.jpg View Image: ScreenHunter_284 Aug. 12 19.55.jpg View Image: ScreenHunter_285 Aug. 12 19.55.jpg

I see you have graph paper.
You must be plotting something
lol

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#5 2013-08-12 18:51:03

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: some problems

hi

I've got to go out very soon, so I'll just look at Q1 for now.

See diagram.  I've put on an extra line XYZ.  How long is XY?  How long is YZ?

Bob

View Image: cool1.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2013-08-12 21:31:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: some problems

Hi cooljackiec;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2013-08-13 06:38:00

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: some problems

hi bobbym,  I've got methods for 2 and 3, but I'm waiting for some feedback on Q1 from the OP.  smile

Seems we've got all five sorted between us.

I haven't gone as far as answers .... I thought he could do that step.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2013-08-13 06:54:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: some problems

Hi;

Okay, then this is done.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9 2013-08-13 07:07:19

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: some problems

Yes.  Just one thing missing.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2013-08-13 12:58:43

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: some problems

yz=xyz-radius of semicircle??

am i supposed to bash with substitution?


I see you have graph paper.
You must be plotting something
lol

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#11 2013-08-13 18:24:00

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: some problems

In the triangle GYZ, YZ is the hypotenuse.  and XY is, yes, the radius of the circle.

So that should enable you to get the total length of the line = size of big square.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2013-08-14 12:43:07

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: some problems

10 + 5sqrt2. derp how did i not see that?!?!?!


how baout 2 and 3?


I see you have graph paper.
You must be plotting something
lol

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#13 2013-08-14 19:29:38

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: some problems

Q1 correct.  Well done!

derp how did i not see that?!?!?!

It can happen to us all.  I nearly messed up an exam because I hadn't noticed that the length of a radius on one side of a circle was the same size as the radius on the other side of the same circle.  doh!

Q2  Call the point where XR and YS cross, point Z.

Triangles ZXY and ZRS are similar.  This is because they have a common angle at Z and XY is parallel to SR.

So If you call the height of ZXY k then ZSR has height 4k (because the ratio of sides is 3:12)

So the height (distance) between XY and SR is 5k.

Now look at triangles ZXY and ZPQ.  These are similar in the ratio k:6k so now you can calculate PQ.

Q3.  I have made a diagram and labelled the points.

PVU is 90 as PV is a tangent

PWS is 90 as WX is the distance you are required to find.

So triangles PVU and PWS are similar.

So you can use the ratio of sides to work out WS, and then WX is easy.

Hope that helps,

Bob

T is the centre of a another circle, diameter PU that goes through V.  I thought I needed this circle too, but, it turns out I don't.  Interesting though.  smile

View Image: cool3.gif

Last edited by bob bundy (2014-08-10 05:27:31)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2013-08-19 04:04:26

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: some problems

thanks, i got both of them.

Let ABCD be a square, and let M and N be the midpoints of

and
, respectively. Find
.

Triangle ABC has side lengths AB = 9, AC = 10, and BC = 17. Let X be the intersection of the angle bisector of \angle A with side \overline{BC}, and let Y be the foot of the perpendicular from X to side \overline{AC}. Compute the length of \overline{XY}.

Equilateral triangle ABC and a circle with center O are constructed such that \overline{BC} is a chord of the circle and point A is the circumcenter of \triangle BCO in its interior. If the area of circle with center O is 48\pi, then what is the area of triangle ABC?

In a triangle ABC, take point D on \overline{BC} such that DB = 14, DA = 13, DC = 4, and the circumcircles of triangles ADB and ADC have the same radius. Find the area of triangle ABC.

Let

denote the circular region bounded by x^2 + y^2 = 36. The lines x = 4 and y = 3 partition
into four regions
. Let
denote the area of region
If
then compute


I see you have graph paper.
You must be plotting something
lol

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#15 2013-08-19 05:28:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: some problems

Hi


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#16 2013-08-19 06:59:48

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: some problems

thanks!!


I see you have graph paper.
You must be plotting something
lol

Offline

#17 2013-08-19 08:39:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: some problems

Hi;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#18 2013-08-20 14:43:50

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: some problems

can you do 3?

i appreciate your help


I see you have graph paper.
You must be plotting something
lol

Offline

#19 2013-08-20 18:02:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: some problems

Hi;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#20 2013-08-21 07:29:02

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: some problems

final one!

View Image: ScreenHunter_286 Aug. 21 12.28.jpg

I see you have graph paper.
You must be plotting something
lol

Offline

#21 2013-08-21 07:41:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: some problems

Hi;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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