Question

Find the value of x. Enter only your numerical value for x

Answer 1

x = 3

Explanation:

Equating the secants :

• 10 (10 + 5x + 2) = 9 (9 + 7x)
• 50x + 120 = 81 + 63x
• 63x - 50x = 120 - 81
• 13x = 39
• x = 3

Answer 2

3

Explanation:

Theorem:

If two secants intersect outside a circle, then the product of the length of the exterior segment of one secant and the length of that secant equals the product of the corresponding parts of the other secant.

In this case:

10 × (10 + 5x + 2) = 9 × (9 + 7x)

10(5x + 12) = 9(7x + 9)

50x + 120 = 63x + 81

-13x = -39

x = 3