Question
Circle A is inscribed in a quadrilateral. What is the perimeter of the quadrilateral?
A circle is shown within a parallelogram. The circle has center point A. The circle's circumference intersects all sides of the inside of the parallelogram.• The top side of the parallelogram is labeled 3 millimeters above the circle.
• The area above and to the right of the circle is labeled 12 millimeters.
• The bottom side of the parallelogram is labeled 2 point 5 millimeters below the circle and 7 point 5 millimeters to the bottom left of the circle.
(1 point)
Responses
25 mm
25 mm
50 mm
50 mm
60 mm
60 mm
150 mm
150 mm
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To find the perimeter of the quadrilateral, we need to add up the lengths of all four sides.
Let's label the points where the circle intersects the sides of the parallelogram as B, C, D, and E.
By symmetry, we can see that BC and DE are equal in length. Let's call this length x.
The top side of the parallelogram is labeled 3 millimeters above the circle, so the length of BD is (x + 3) millimeters.
The bottom side of the parallelogram is labeled 2.5 millimeters below the circle and 7.5 millimeters to the bottom left of the circle. So, the length of CE is (x + 2.5 + 7.5) millimeters, which simplifies to (x + 10) millimeters.
The length of AD is simply the diameter of the circle, which is equal to 2 times the radius.
The radius of the circle is half the length of BD, so it is (1/2)(x + 3) millimeters.
Therefore, the diameter of the circle is 2(x + 3) millimeters, and the length of AD is 2(x + 3) millimeters.
The perimeter of the quadrilateral is P = BD + AD + CE + DE.
P = (x + 3) + 2(x + 3) + (x + 10) + x
P = 5x + 16 millimeters.
We don't have enough information to solve for x, so we cannot determine the specific perimeter of the quadrilateral.
please pick one option
Based on the given options, the correct answer would be:
50 mm