# Question Video: Finding the Length of a Chord in a Circle Mathematics

Given that 𝐸𝐶 = 4, 𝐸𝐷 = 15, and 𝐸𝐵 = 6, find the length of the line segment 𝐸𝐴.

02:06

### Video Transcript

Given that 𝐸𝐶 equals four, 𝐸𝐷 equals 15, and 𝐸𝐵 equals six, find the length of the line segment 𝐸𝐴.

Let’s look at the diagram more closely. We can see that it consists of a circle, in which there are two intersecting chords. They’re the lines 𝐴𝐵 and 𝐶𝐷. We’ve also been given various lengths that we can add to our diagram. The length of the line segment 𝐸𝐶 is four. The length of the line segment 𝐸𝐷 is 15. And the length of the line segment 𝐸𝐵 is six.

We’re asked to work out the length of the line segment 𝐸𝐴. So we need to recall the relationship that exists between the lengths of the line segments of intersecting chords. We remember that “if two chords intersect in a circle, then the products of the lengths of the chord segments are equal.”

Our two chords intersect inside the circle at the point 𝐸. So we have that the product of the lengths of the chord segments of the orange chord, that’s 𝐸𝐴 multiplied by 𝐸𝐵, is equal to the product of the length of the chord segment of the pink cord. That’s 𝐸𝐶 multiplied by 𝐸𝐷. We know the lengths of the chord segments 𝐸𝐵, 𝐸𝐶, and 𝐸𝐷. So we can substitute their values into this equation given that the length of the chord segment 𝐸𝐴 multiplied by six is equal to four multiplied by 15.

Dividing both sides of this equation through by six gives a calculation that we can use to find the length of the chord segment 𝐸𝐴. It’s equal to four multiplied by 15 over six. Four multiplied by 15 is equal to 60. And 60 divided by six is equal to 10.

Using then the relationship between the lengths of chord segments for chords which intersect inside a circle, we found that the length of the chord segment 𝐸𝐴 is 10. There’re no units for this as there were no units for the original measurements we were given for the other three chord segments.

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