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What is the radius of this quarter-circle?

 

 Jan 10, 2020
 #1
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Hint:

 

Use variables X and Y for the side lengths of the given rectangle.

 

All radii are congruent. One of the diagonal of the rectangle is a radii

 

So

 

x+4 = y + 2

 

x2 + y2 = x + 4  (Pythagorean theorem to find the diagonal)

 Jan 10, 2020
 #2
avatar+107405 
+1

Note that one side of the rectangle = r -2

And the other side  = r - 4

 

Using the Pythagorean Theorem  we have that

 

(r - 2)^2 + ( r - 4)^2 = r^2     simplify

 

r^2 - 4r + 4 + r^2 - 8r +16  = r^2

 

2r^2  -12r + 20  = r^2

 

r^2 - 12r + 20    = 0     factor

 

(r - 10) ( r - 2)  = 0

 

Setting each factor to  0  and solving for r we get that   r =  2  (reject)   or  r =  10 (accept)

 

 

 

cool cool cool

 Jan 11, 2020
 #3
avatar+370 
+1

I was looking for the angle whose cosine value is for 2 units larger then the value of sine.

And these numbers popped up:    0.8 and 0.6        sin(36.87°) = 0.6     cos(36.87°) = 0.8

I multiplied these numbers by 10,  and got the sides of a rectangle: a = 6   and  b = 8

Diagonal   d = r                      r² = a²+ b²           r = 10      indecision

 Jan 11, 2020
edited by Dragan  Jan 11, 2020

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