Question

How many units is x ????

Answer 1

Remark

ED is a tangent line. EF is a secant line. Secants and Tangents are related by the formula Tangent length ^2 from a point = length from the same point to the closest part of the circumfrence * the entire length of the secant.

Formula

Putting that long sentence into symbols

ED^2 = EG * EF

Givens

EG = 9

EF = 9 + x

ED = 12

Sub and solve

12^2 = 9*(9 + x) You can either divide by 9 or remove the brackets. I will divide by 9

144 / 9 = 9 * (9 + x) /9

16 = x + 9 Subtract 9 from both sides.

x = 7

x = 7 units. <<<<<<<< Answer

Answer 2

9(9+x) = 12^2

81 + 9x = 144

9x = 63

x = 7

answer

x = 7 units