# Question Video: Determining Which Chord Is Longer in a Circle Based on the Lengths of Perpendicular Chords Mathematics

Suppose that π΅πΆ = 8 cm and π΅π΄ = 7 cm. Which of the following is true? [A] π·π = ππ [B] π·π > ππ [C] π·π < ππ

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### Video Transcript

Suppose that π΅πΆ equals eight centimeters and π΅π΄ equals seven centimeters. Which of the following is true? Is it (A) π·π is equal to ππ, (B) π·π is greater than ππ, or (C) π·π is less than ππ?

Letβs begin by adding the lengths π΅πΆ and π΅π΄ to our diagram. These are the distances from the chords π·π and ππ, respectively, to the center of the circle π΅. 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 ππ is seven centimeters from the center. This is the length of π΅π΄. The chord π·π, on the other hand, is eight centimeters from the center. This means that ππ is closer to the center of the circle than π·π. As this chord will have a greater length, we can conclude that ππ is greater than π·π. From the three options listed, the correct answer is option (C) π·π is less than ππ.