Begin by connecting the outer ends of segments of length 5 and x with a diameter. What can be said about the triangles formed?
5
Practice makes perfect
We are asked to find the value of x in the given diagram. First, we can connect the outer ends of segments of length 5 and x with a diameter.
Look closely at the two triangles that have formed. Both are right triangles since the chords are perpendicular to the segment that goes through the center. In the graph we see that the shorter legs are congruent. What's more, the lengths of triangles' hypotenuses are the same since both are equal to the radius.
By the Side-Angle-Side Congruence Theorem, the triangles are congruent. Therefore, their corresponding sides are the same length. In particular, this applies to the legs of length 5 and x.
x= 5
