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Thanks Advance!

 

 May 14, 2020
 #1
avatar+111321 
+3

Perimeter  = 2 (3 + 5 + 4 + 4)  = 2 ( 16)  =  32 cm

 

 

cool cool cool

 May 14, 2020
 #2
avatar+241 
+1

Cphill how did you get a second 4?

Mathisgood  May 14, 2020
 #4
avatar+1498 
+2

My gut tells me that AD is 3*2 = 6...

 

So 2(3+3+4+5) = 2*15 = 30

 

Cphill probably meant AD is 2*4 

hugomimihu  May 14, 2020
 #3
avatar+111321 
+3

Yeah....that's a little confusing

 

Note  that if angle B  = angle D, than the tangents drawn from D  have  the same length as the tangents drawn from B

 

The tangents from B both have the length of 4 cm

 

So....the two tangents drawn from D have the same length

 

And the tangents drawn from A  = 3cm

 

And the tangents drawn from C  = 5cm

 

So

 

[ tangents drawn from B + tangents drawn from D  + tangents drawn from A  + tangents drawn from C] =

 

[  (4 + 4)   + (4 + 4)  + (3 + 3)  +(5 + 5) ]  =

 

[ 8  +  8   +  6  +  10]  =

 

32 cm

 

 

cool cool cool

 May 14, 2020
 #5
avatar+1498 
+2

Also it appears that the radius(based on image) is 4.5 since 4 and 5 seem to be equally above/below it.

 

In that case the diameter is 9.

 

Hmm.

hugomimihu  May 14, 2020
 #6
avatar+241 
+1

Thanks Cphill and Hugo!

Mathisgood  May 14, 2020
 #7
avatar+111321 
+3

Consider this, hugo

 

[ Remember  that tangents drawn to a circle  from an exterior point have equal lemgths ]

 

If we draw  radii  to the  midpoints  of AD . DC, AB,BC  we will create  congruent quadrilaterals

 

Therefore....the midpoint  of BC to B  = 4

And this is a tangent

And the midpoint of AB to B  is  a tangent with the same length

 

But  since we have congruent quadrilaterals then the tangents drawn from D  to the circle will have the same length as those drawn from B to the circle =  4

 

And the tangents drawn from A  have the same length  = 3

And the tangents drawn from C have the same length = 5

 

So...the perimeter  is just  2 [ 4 + 4 + 5 + 3]  =  32 cm

 

 

cool cool cool

 May 14, 2020
 #8
avatar+1498 
+2

Oh I get it now thanks for the explanation!!!

hugomimihu  May 14, 2020
 #9
avatar+111321 
+2

OK.....no prob......this one is confusing   !!!!

 

 

cool cool cool

CPhill  May 14, 2020

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