A chord, distant 2cm from the centre, of a circle is 18cm long. Calculate the length of a chord of the same circle which is 6cm distant from the centre.
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To calculate the length of a chord of a circle that is 6cm distant from the center, we can use the following approach:
1. Given: A chord is 18cm long and distant 2cm from the center of the circle.
2. Let's use the property that says if two chords in a circle are equidistant from the center, then they are equal in length.
3. Since the given chord is 2cm distant from the center, we will divide the given length of the chord by the distance from the center to find the ratio.
Length of given chord / Distance from center = Length of unknown chord / Distance from center
18cm / 2cm = Length of unknown chord / 6cm
4. Now, let's solve for the unknown chord length:
(18cm * 6cm) / 2cm = Length of unknown chord
(108cm) / 2cm = Length of unknown chord
Length of unknown chord = 54cm
Therefore, the length of the chord that is 6cm distant from the center is 54cm.