# straight line

## Length of hypotenuse of a right triangle of known area in the xy-plane

**Problem**

For triangle *BOA*, *B* is on the *y*-axis, *O* is the origin, and *A* is on the *x*-axis. Point *C*(5, 2) is on the line *AB*. Find the length of *AB* if the area of the triangle is 36 unit^{2}.

A. 24.31 units | C. 13.42 units |

B. 18.30 units | D. 10.80 units |

## 01 - Circle tangent to a given line and center at another given line

**Problem 1**

A circle is tangent to the line 2*x* - *y* + 1 = 0 at the point (2, 5) and the center is on the line *x* + *y* = 9. Find the equation of the circle.