Question

Given a circle with radius of 3 cm. We drew two chords that are perpendicular to each other. One chord is 1 cm, the other is 2 cm away from the centre of the circle. Let us denote the areas of the four parts with x, y.z. v. What will be the area of (x+z)-(y+v)?

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Answer 1

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Answer:

8 cm²

Explanation:

If you reflect the drawn lines across the center of the circle, you can determine that the central rectangle is 2 cm wide and 4 cm high. Its area is the difference described by the expression ...

(x +z) -(y +v) = (2 cm)(4 cm) = 8 cm²

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The attached figure shows the areas of the individual non-overlapping regions. Comparing this to the original drawing you can see that the labels are shown properly.

The four upper right areas total to x. The two of those above the horizontal line total to v, so the right-center two areas are x-v. The rightmost center area is y-z, so the central rectangle is (x -v) -(y -z) = (x +z) -(y +v).