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oh geez, did he get banned?

angle ABC  = 90°

Note that AC = sqrt (3^2 + 5^2)  = sqrt (34)

Area of ABC =  (1/2) (AB) (BC)  = (1/2) (3) (5)  = 7.5

Height of ABC  can be found as

2* area of ABC / AC   =  2 * 7.5  /  sqrt (34)  =     15 / sqrt (34)

And triangles  ABC and  WBZ are similar

Call the side of the square  S

Base of ABC / Height of ABC =  Base of WBZ / Height of WBZ

sqrt (34) / ( 15 /sqrt (34) ) =  S  / (15/sqrt (34)  - S)

34 / 15  = S / ( 15/sqrt (34) - S)

(34/15) ( 15 /sqrt (34) - S)  =  S

sqrt (34)  - ( 34/15)S = S

sqrt (34) = S ( 1 + 34/15)

S =  sqrt (34)  / ( 1 + 34 /15)  =  15 *  sqrt (34)  / ( 49)  =  (15/49)sqrt (34) ≈ 1.785

very neat solution BB!

ya, like this Newboi guy or whatever. he kept posting inappropiate stuff

   A

   4 

  X

                            8            10

7             

                                Y

 B                                  C

Area of   ABC =  (1/2) ( AB) (AC) sin BAC =  (1/2) ( 7)(10)  sin BAC

Area of  AXY  =  (1/2) (AX) ( AY) si BAC =   (1/2) (4) ( 8) sin BAC

[ AXY ] /  [ ABC ]  =   (4 * 8 )  / ( 7 * 10) =   32 / 70  =    16 /  35

Possible triangles

2 7 7

3 6 7

4 5 7

4 6 6

5 5 6

1 + 3 +  ....+ 199

Number of terms    =   (199 - 1)  / 2  + 1    =  100

Sum  =   (1 + 199) / ( 100 / 2)  =   10000

2 + 4 + ......+ 202

Number of terms =   (200 - 2) / 2 + 1 =   101

Sum =  (2 + 202)  * (101) /2  =  10302

10000 /  10302  =   5000 / 5151

See asinus's   answer  here :  https://web2.0calc.com/questions/geometry_96592

Very nice , guys   !!!!!

hmmmmm

Right, but the area of the bottom 2 units is NOT 1/3 of the total area of the triangle. 

that was a copied answer from wiseowl

a wise owl told me once

In order for the area of triangle XYD to be at most 12, the height of triangle XYD is at most 2.  The height of triangle XYD can be 6, so the probability is 2/6 = 1/3.

WISEOWL's answer, which was voted as a 'best answer'

Wouldn't the probability be the \({\text{successful region} \over \text{total region}} = {[XYAB] \over \triangle XYZ}\)

The area of the successful region is \((2 \times 8) + (4 \times 2 \div 2) = 20\), and the area of the total region is \(12 \times 6 \div 2 = 36\)

So the probability is \({20 \over 36} = \color{brown}\boxed{5 \over 9}\)

LOL

I saw you doing your answer, and I was like, I gotta beat BuilderBoi

Let \(CP = x\) and \(DP = y\) and let the center of the circle be o.

We have the following system from the intersecting chord theorem: 

\(xy = 40 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (i)\)

\(x + y = 13 \ \ \ \ \ \ \ \ \ (ii)\)  

Solving for x and y, we find that \(x = 8\) and \(y = 5\).

P is 3 units away from the midpoint of AB and 1.5 units away from the midpoint of CD.

This means that the distance is \(\sqrt{3^2 + 1.5^2} = \sqrt{11.25} = \color{brown}\boxed{3 \sqrt 5 \over 2}\)

Here's a graph: 

There’s probably more than one way to solve this. Here’s how I would go about it.

From the intersecting chords theorem, you know that CPxDP = 4x10. You also know that CP+DP=13 (=CD). You now have two equations involving CP and DP.

Combining the two equations gives you a quadratic expression which when solved gives you CP= 5 and DP=8.

The distance from the midpoint of CD to P can be found to be 1.5.

The distance from the midpoint of AB to P can be found to be 3.0.

The distance of P to the center of the circle is the same as the diagonal of a rectangle of sides 1.5 and 3.0 which can be evaluated from the Pythagorean theorem (approximately 3.354).

quora

CPhill, I saw you conducting yur ans

why u stopp

well, its wrong

I drew a diagram, and worked it out.  My friend got the same answer.

Simplify (1+3+5+...+199) / (2+4+6+...+198+200+202)==[2n - 1] / [2n] ==10,000 / 10,302

5,000 / 5,151

XY  = the base of the triangle  =  12

Then the altitude cannot be more than  2

After some reflection, I believe that BuilderBoi's answer is correct  !!!

D can fall ANYWHERE in the area of the trapezoidal area given by

(1/2) (2) (8 + 12)    =  20

So.....the probability  is     20  /  36  =   5/9  

THX BuilderBoi for  helping  me to  see this  !!!!

yur mom

When \(x = 0\), \(y = 0x + 0x + 7 = 7\), meaning \(c = 7\)

Likewise, when \(x = 6\), \(y = 36a + 6b + 7 = 7\), meaning \( 36a + 6b = 0 \)

When \(x = 3\), \(y = 9a + 3b + 7 = 1 \), meaning \(9a + 3b = -6\)

So now, we have this system, and we need to solve for a and b: 

\(9a + 3b = -6\)

\(36a + 6b = 0 \)