Question

Can someone plz help me with 11,12,13 plz show work

Answer 1

Answer:

  11.  x = -3+√37 ≈ 3.08276

  12.  x = 11.2

  13.  x = -6 +6√5 ≈ 7.41641

Step-by-step explanation:

In each case, the relation of interest is ...

  (distance to circle near) × (distance to circle far) = (distance to circle near) × (distance to circle far)

When there is only one point of intersection of the secant with the circle—because it is a tangent—then the product is the square of the length of the tangent.

11. 2(2+12) = x(x +6)

  x² +6x -28 = 0

  (x +3)² -37 = 0

  x = -3+√37 ≈ 3.08276

12. 5(5+x) = 9(9)

  5x +25 = 81

  x = 56/5 = 11.2

13. x(x +12) = 12(12)

  x² +12x -144 = 0

  (x +6)² -180 = 0

  x = -6 +√180 ≈ 7.41641

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Comment on this secant rule

This rule turns out to apply whether the point of intersection of the secant lines is outside the circle (as in these problems) or inside the circle (as in problem 9). The product of the two distances from the point of intersection to the circle is a constant for a given pair of intersecting secants/chords.