Respuesta :
The diameter of this circle has length of 65 when it is inscribed in a circle is a quadrilateral.
What is meant by diameter?
The straight line that runs through the center of a round shape or object from one point on one edge to another: The diameter is twice as large as the radius. The pond is six feet across. Both definitions hold true for the diameter of a sphere.
We note that 25²+60²=65² and 39²+52²=65²
Let [tex]\bar{AB}[/tex]=25, [tex]\bar{BC}[/tex]=39, [tex]\bar{CD}[/tex]=52, [tex]\bar{DA}[/tex]=60
Let [tex]\bar{BD}[/tex]=x and ∠DAB=y
x²=25²+60²-3000cos(y)
x²=39²+52²-4056cos(180-y)
We obtain by performing some computation x²=4225-3000cos(y) and x²=4225-4056cos(y).
4056cos(y)=3000cos(180-y)
cos(180-y)=-cos(y)
So, by substituting we get 4056cos(y)= -3000cos(y)
cos(y)=0 or y=90.
∠BAD=90 and ∠BCD=90.
The diameter of a right triangle inscribed in a circle is the hypotenuse.
This means that the diameter is √4225=65
Therefore, the diameter of this circle has length of 65.
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