Multiple choice

A circle is tangent to the x-axis at the point (5, 0) and passes through the point (1, 8). What is the radius of the circle?

  1. 3

  2. 4

  3. 5

  4. 6
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C Correct answer
Explanation

Circle tangent to x-axis at (5, 0) has center (5, r). Equation: (x - 5)^2 + (y - r)^2 = r^2. Passes through (1, 8): (1 - 5)^2 + (8 - r)^2 = r^2 => 16 + 64 - 16r + r^2 = r^2 => 80 = 16r => r = 5.

AI explanation

Because the circle is tangent to the x-axis at (5, 0), its center must be at (5, r). The distance from the center (5, r) to the point (1, 8) equals the radius r. Using the distance formula, we set r equal to the square root of ((5 - 1)^2 + (r - 8)^2). Squaring both sides gives r^2 = 16 + r^2 - 16r + 64, which simplifies to 16r = 80. Therefore, the radius of the circle is 5.

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