Answer:
The correct option is 3. The perimeter of kite OBDE is 27 units.
Step-by-step explanation:
From the figure it is clear that the triangle ABC is right angled triangle.
According to Pythagoras theorem,
[tex]hypotenuse^2=perpendicular^2+base^2[/tex]
Using Pythagoras theorem, we get
[tex]AB^2=AC^2+BC^2[/tex]
[tex]AB=\sqrt{(15)^2+(8)^2}[/tex]
[tex]AB=17[/tex]
The diameter of circle of is 17 units. So, the radius of the circle is
[tex]\frac{17}{2}=8.5[/tex]
Angle DBO and DEO are right angles it means DB and DE are tangent.
According to the circle tangent theorem the length of tangent from the same point are equal.
[tex]DB=DE=5[/tex]
[tex]r=OB=OE=8.5[/tex]
Perimeter of kite OBDE is
[tex]Perimeter(OBDE)=OB+DB+DE+OE[/tex]
[tex]Perimeter(OBDE)=8.5+5+5+0.8=27[/tex]
The perimeter of kite OBDE is 27 units. Therefore the correct option is 3.
