Question

Solve for x. Show your work.

Answer 1

First image x=1

Second image x=4

*Note= The two lines of measurement are always the same.

Answer 2

Figure 1: x=7

Figure 2: x=2

Explanation:

Figure 1:

In a given circle, two secant intersect externally.

Intersecting Secants Theorem: If two secants intersect externally then product of their segments is constant.

Thus,

`(x+5)* 5=(4+6)* 6`

`5x+25=60`

`5x=60-25`

`5x=35`

`x=7`

Figure 2:

Using same theorem as above.

`(5+3)* 3=(x+4)* 4`

`24=4x+16`

`4x=24-16`

`4x=8`

`x=2`