Video Transcript
Find the value of 𝑥.
In the diagram, we can see that we have a circle and two lines, 𝐴𝐵 and 𝐴𝐶, each
of which are tangents to the circle. The two tangents have been drawn from the same exterior point, point 𝐴. One of the key properties of tangents of circles is that tangents drawn from the same
exterior point are equal in length. So we know the line segment 𝐴𝐶 is equal in length to the line segment 𝐴𝐵. We’ve been given the length of 𝐴𝐵; it’s 21 centimeters. And we’ve been given an expression for the length of 𝐴𝐶; it’s two 𝑥 plus five
centimeters. So, equating these, we can form an equation: two 𝑥 plus five is equal to 21.
We can now solve this equation to determine the value of 𝑥. We first subtract five from each side, giving us two 𝑥 equals 16, and then divide by
two, giving us 𝑥 equals eight. Thus, by using the key property that tangents drawn from the same exterior point are
equal in length, we’ve found the value of 𝑥. 𝑥 is equal to eight.
