# Question Video: Finding Measures of Arcs Using the Measure of the Central Angle Mathematics • 11th Grade

Given a circle 𝑀 with two chords 𝐴𝐷 and 𝐵𝐶 that have equal lengths and the arc 𝐴𝐷 with a length of 5 cm, what is the length of the arc 𝐵𝐶?

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### Video Transcript

Given a circle 𝑀 with two chords 𝐴𝐷 and 𝐵𝐶 that have equal lengths and the arc from 𝐴 to 𝐷 with a length of five centimeters, what is the length of the arc from 𝐵 to 𝐶?

We’re given two chords in a circle with equal lengths, 𝐴𝐷 and 𝐵𝐶. We can highlight these chords on our diagram and the fact that they have equal length. We’re also told that the length of the minor arc from 𝐴 to 𝐷 is five centimeters. We can also add this to our diagram. We need to use this to determine the length of the minor arc from 𝐵 to 𝐶. We can answer this question geometrically by noticing 𝐴𝑀, 𝐵𝑀, 𝐶𝑀, and 𝐷𝑀 are radii of the circle, so they have equal length. This means that triangles 𝐴𝑀𝐷 and 𝐵𝑀𝐶 are congruent. So the measures of the central angles of these two arcs are equal.

Then, since the central angles of these two arcs are equal, the lengths are equal, meaning that 𝐵𝐶 has length five centimeters. However, we could’ve also answered this question by just recalling if the chords between two points on a circle are equal, then their arc lengths are also equal. Using either method, we were able to show the length of the minor arc from 𝐵 to 𝐶 is five centimeters.