Question

What is the value of x?​

Answer 1

5.6

Explanation:

We want to find the value of x, which is part of the segment that includes the length 10.

We need to use Power of Points, one property of which essentially says that if we have two intersecting chords such that they are each cut into two parts to make a and b, and c and d, then ab = cd (see attachment).

Here, we can say that a = 10, b = x, c = 7, and d = 8. Plug these in:

ab = cd

10 * x = 7 * 8

10x = 56

x = 56/10 = 5.6

The answer is 5.6.

Answer 2

Each diagonal has two parts (a, b, c, and d).

The formula is ab = cd

We have the values:

a = 10

b = x

c = 8

d = 7

Put these in the formula:

10x = (8)(7)

Solve for x.

10x = (8)(7)

10x = 56

10x/10 = 56/10

x = 5.6

Therefore, the answer is x = 5.6

Best of Luck!