10.6 & 10.7 Notes

1. 10.6 & 10.7 Notes

2. 10.6 Finding Segment Lengths in Circles • Segments of the chord- when 2 chords intersect in the interior of a circle, each chord is divided into 2 segments

3. Segments of Chords Theorem • If 2 chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

4. Example • Find x.

5. Segments of Secants Theorem • If 2 secant segments share the same endpoint outside the circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.

6. Example • Find x.

7. Segments of Secants and Tangents Theorems • If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the lengths of the tangent segment.

8. Example • Solve for x.

9. 10.7 Writing and Graphing Equations of Circles • (x,y) represents a point on a circle • By the Pythagorean Theorem, x2 + y2 = r2 when the center is at the origin.

10. Standard Equation of a Circle • Center of circle is at (h,k) • r2 = (x - h)2 + (y - k)2

11. Example • Write the equation of the circle.

12. Example • Write the standard equation of a circle with center (-2,3) and radius 3.8.

13. Example • Point (8,-1) is on the circle with center (4,2). Write the standard equation of the circle.

14. Example • The equation of a circle is (x + 1)2 + (y – 3)2 = 4. Graph the circle.

15. Example • Three forest ranger stations are located at A(-3,2), B(2,2) and C(-1,-1.5). A fire breaks out 2 miles from A, 3 miles from B and 3.5 miles from C. Find the location of the fire.