Question

Find the radius of a circle using the Pythagorean theorem, given that the center is at (11, -3) and the point (3, 12) lies on the circle.

Answer 1

Center: (11, -3)

Point: (3,12)

Radius?

The Pythagorean theorem using the circle is:

`\begin{gathered} (x\text{ -a\rparen}^2\text{ + \lparen y -b\rparen }^2=\text{ r}^2 \\ Center\text{ \lparen a, b\rparen = \lparen11. -3\rparen} \\ Point\text{ \lparen x, y\rparen= \lparen3, 12\rparen} \\ \\ (3\text{ - 11\rparen}^2\text{ + \lparen12 - \lparen-3\rparen\rparen}^2=\text{ r}^2 \\ (\text{ -8\rparen}^2\text{ + \lparen12 + 3\rparen}^2=\text{ r}^2 \\ 64\text{ + \lparen15\rparen}^2=\text{ r}^2 \\ 64\text{ + 225= r}^2 \\ 289=\text{ r}^2 \\ \sqrt{289=\text{ r}} \\ 17=\text{ r} \end{gathered}`

The radius of the circle is 17.