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If the center of a circle is (4,2) and a point on the circle is (12,6), what is the radius?

If the center of a circle is (4,2)(4,2) and a point on the circle is (12,6)(12,6), what is the radius?

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Full solution

Q. If the center of a circle is (4,2)(4,2) and a point on the circle is (12,6)(12,6), what is the radius?
  1. Identify Formula: Identify the formula for the distance between two points, which gives the radius of the circle.\newlineDistance formula: (x2−x1)2+(y2−y1)2 \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
  2. Substitute Coordinates: Substitute the coordinates of the center (44,22) and the point on the circle (1212,66) into the distance formula.\newlineCalculate: (12−4)2+(6−2)2 \sqrt{(12 - 4)^2 + (6 - 2)^2}
  3. Simplify Calculations: Simplify the calculations inside the square root.\newlineCalculate: (8)2+(4)2=64+16 \sqrt{(8)^2 + (4)^2} = \sqrt{64 + 16}
  4. Add Values and Find Square Root: Add the values under the square root and find the square root.\newlineCalculate: 80 \sqrt{80} \newlineThis simplifies to 45 4\sqrt{5} , which is approximately 88.944944.

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