Question

Select one: a. 4 b.5 c. 6 d. 7

Answer 1

Answer:

C

Step-by-step explanation:

Given 2 secants intersect a circle from a point outside the circle, then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

x(x + 10 + x) = 6(6 + 10 + x)

x(2x + 10) = 6(16 + x) ← distribute parenthesis on both sides

2x² + 10x = 96 + 6x ← subtract 96 + 6x from both sides

2x² + 4x - 96 = 0 ← in standard form

Divide through by 2

x² + 2x - 48 = 0 ← factor the left side

(x + 8)(x - 6) = 0

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

However x > 0 ⇒ x = 6 → C