Video: Finding the Radius of a Circle given the Length of Its Longest Chord

If the length of the longest chord in a circle is 310 m, what is its radius?

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Video Transcript

If the length of the longest chord in a circle is 310 metres, what is its radius?

To start, let’s recall what the chord of a circle actually is. A chord is a segment that connects two points on the circumference of a circle. So, we could have a shorter length chord or a longer length chord. Here, we’re told that the longest chord in this circle is 310 metres. But where exactly would the longest chord be? Well, the longest chord will pass right through the centre of the circle. The special name given to the longest chord in a circle is one that we’re already familiar with. And that’s the diameter of the circle.

It might be worth making a note that when a chord passes through the centre of a circle, it’s the longest chord, and it’s called the diameter. So, now that we know that the longest chord is actually the diameter, then finding the radius becomes a simpler prospect. Since the radius is half of the diameter, then for our diameter of 310 metres, we calculate half of that. Giving us 155 metres since half of 300 is 150, and half of 10 is five. So, the radius is 155 metres.

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