A circle is shown. The shelf is represented by a chord and the brace goes from the chord to to a point on the circle. The brace line is extended up to form a diameter.

Custom drapes are being fitted for a large circular window. It is difficult to get these measurements, but the window has an 8 ft horizontal shelf with a 2 ft brace that sits in the frame. If the brace is extended upward, it would go through the center of the shelf and the circle. What is the diameter of the window?

Diameter = feet

The diameter of a circle is the line segment that divides the circle into two equal halves. The diameter divides the circle into semicircles. Also, the diameter of a circle is twice the length of the radius of a circle.

If we know the length of the radius, we can determine the length of the diameter of a circle by multiplying the radius by two. On the other hand, if we know the length of the diameter, to find the length of the radius, divide the diameter by 2.

The image of the circle showing the shelf and the brace line, which is the diameter are shown below.

To find the diameter of the window, add the length of the horizontal shelf and length of the brace. Thus:

Length of the diameter of the window = 8 + 2

Length of the diameter of the window = 10 ft

Thus, the length of the diameter formed is: 10 ft.

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