Question

Calculate the length of the
segment labeled x.
Х
8
A-
12
20

Answer 1

Answer:

x = 8.


Explanation:

The external secent line theorem says,
S1E1 = S2E2.

Secent s1 and s2.
External E1 and E2.

E2 = 12.
S2 = 32

S1 = 8 + x.
E1 = 8.

12*32 = 8(8+x).
384 = 8(8+x).
48 = 8+x
x = 40.

Answer 2

x = 40

Explanation:

Given 2 secants from an external point to the circle, then

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

8(8 + x) = 12(12 + 20)

8(8 + x) = 12 × 32 = 384 ( divide both sides by 8 )

8 + x = 48 ( subtract 8 from both sides )

x = 40