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circle passing through points C, D and G was automatically constructed for you. How could you construct a circle passing through the three points?

Question

circle passing through points C, D and G was automatically constructed for you. How could you construct a circle passing through the three points?

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Solution

To construct a circle passing through three points C, D, and G, follow these steps:

  1. Draw a straight line connecting points C and D. Do the same for points C and G. You should now have two lines intersecting at point C.

  2. Find the midpoint of each line. This is done by measuring the total length of each line and dividing by two. Mark these midpoints.

  3. Draw a line perpendicular to each of the original lines, passing through their respective midpoints. These are called the perpendicular bisectors. They should intersect at a point, which will be the center of the circle.

  4. Use a compass to draw a circle from the intersection point (center of the circle) to any of the three points C, D, or G. The circle should now pass through all three points.

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A circle with center 𝐶 which passes through the point 𝑃 is shown in the given figure.Which of the following best describes how to construct a line that is tangent to the circle at the point 𝑃 using a straightedge and compass?ResponsesConstruct a vertical line passing through point 𝑃.Answer A: Construct a vertical line passing through point P .AConstruct a horizontal line passing through point 𝑃.Answer B: Construct a horizontal line passing through point P .BConstruct a line passing through point 𝐶 that is perpendicular to the line containing points 𝐶 and 𝑃.Answer C: Construct a line passing through point C that is perpendicular to the line containing points C and P .CConstruct a line passing through point 𝑃 that is perpendicular to the line containing points 𝐶 and 𝑃.

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