Suppose that 𝐵𝐶 equals eight
centimeters and 𝐵𝐴 equals seven centimeters. Which of the following is true? Is it (A) 𝐷𝑀 is equal to 𝑋𝑌,
(B) 𝐷𝑀 is greater than 𝑋𝑌, or (C) 𝐷𝑀 is less than 𝑋𝑌?
Let’s begin by adding the lengths
𝐵𝐶 and 𝐵𝐴 to our diagram. These are the distances from the
chords 𝐷𝑀 and 𝑋𝑌, respectively, to the center of the circle 𝐵. We recall that the chord that is
closer to the center of the circle has a greater length. From the diagram, we see that the
chord 𝑋𝑌 is seven centimeters from the center. This is the length of 𝐵𝐴. The chord 𝐷𝑀, on the other hand,
is eight centimeters from the center. This means that 𝑋𝑌 is closer to
the center of the circle than 𝐷𝑀. As this chord will have a greater
length, we can conclude that 𝑋𝑌 is greater than 𝐷𝑀. From the three options listed, the
correct answer is option (C) 𝐷𝑀 is less than 𝑋𝑌.