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## Topic review (newest first)

bobbym
2013-08-22 05:41:02

Hi;

cooljackiec
2013-08-22 05:29:02

final one!

bobbym
2013-08-21 16:02:22

Hi;

cooljackiec
2013-08-21 12:43:50

can you do 3?

i appreciate your help

bobbym
2013-08-20 06:39:11

Hi;

cooljackiec
2013-08-20 04:59:48

thanks!!

bobbym
2013-08-20 03:28:10

Hi

cooljackiec
2013-08-20 02:04:26

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

bob bundy
2013-08-15 17:29:38

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 one unit (choose units so this is true) then ZSR has height 4 units (because the ratio of sides is 3:12)

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

So you can work out MN.

And then 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.

cooljackiec
2013-08-15 10:43:07

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

how baout 2 and 3?

bob bundy
2013-08-14 16:24:00

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

cooljackiec
2013-08-14 10:58:43

yz=xyz-radius of semicircle??

am i supposed to bash with substitution?

bob bundy
2013-08-14 05:07:19

Yes.  Just one thing missing.

Bob

bobbym
2013-08-14 04:54:18

Hi;

Okay, then this is done.

bob bundy
2013-08-14 04:38:00

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

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

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