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I have been thinking about this problem, but I can't get anywhere.

 

The figure shows a circle with A as its center and has a radius of 5.

EC and EF are both tangent to the circle, and DG is a secant line that passes through A and intersects with the circle at G.

∠EDB=90∘, and DB=4.

Find the perimeter of triangle DBA.

 

 Jun 22, 2020
 #1
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Draw CA.

CA will be perpendicular to CDE (radius to tangent).

DB || CA (both perpendicular to EC).

Find point X on CA such that DX || BA.

XA = 4 (DBAX is a parallelogram).

CX = 1.

DX = 5.

Triangle(DCX) is a right triangle   --->   CX2 + CD2  =  DX2   --->   12 + CD2  =  52

   --->   CD  =  sqrt(24)

Triangle(DCA) is a right triangle   --->   DC2 + CA2  =  DA2   --->   [sqrt(24)]2 + 52  =  DA2

   --->   DA  =  7

 

Now, you can find the perimeter of triangle(DBA).

 Jun 22, 2020

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