Question

Two chords intersect with the measures shown in the drawing
What is the value of x?

Answer 1

x = 10.

The intersecting chords theorem states that the product of the segments formed by two intersecting chords are equal. This gives us

6*x = 12*5
6x = 60

Divide both sides by 6:
6x/6 = 60/6
x = 10

Answer 2

By using the property of intersecting chords in a circle, the value of x is 10.

How to find the value of x

To find the value of x, use the property of intersecting chords in a circle. According to this property, when two chords intersect within a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

In this case, we have:

AE * EB = CE * ED

Substitute the given values

5 * 12 = 6 * x

Simplifying the equation:

60 = 6x

To solve for x, divide both sides of the equation by 6:

60 / 6 = x

x = 10

Therefore, the value of x is 10.