Independent practice: tangents of circles Find the value of x in each of the following:
(see picture)

Step-by-step explanation:

9). "Tangent is perpendicular to the radius of a circle"

   By applying Pythagoras theorem in the given triangle,

   x² = 15² + 20²

  x = √625 = 25

10). By applying Pythagoras theorem in the given triangle,

  (r + x)² = r² + 15²

  (8 + x)² = 8² + 225

  8² + x² + 16x = 8² + 225

  x² + 16x = 225

  x² + 16x - 225 = 0

  x² + 25x - 9x - 225 = 0

  x(x + 25) - 9(x + 25) = 0

  (x + 25)(x - 9) = 0

  x = -25, 9

  But x > 0

  Therefore, x = 9 is the answer.

11). By the property of the tangents drawn to the circle from a point,

"Tangents drawn from a point lying outside the circle are equal in measure"

AC = BC

3x + 4 = 40

3x = 36

x = 12

12). By the same property used in question (11)

DE = DC = 4 units

BA = BC = 3 units

x = 4 + 3 = 7 units

step-by-step explanation: