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In a circle, a chord subtends 108deg at the centre. To which of the following is the length of this chord equal?

1. The sum of the chords subtending 36deg and 60deg
2. The sum of the chords subtending 54deg and 54deg
3. The difference of the chords subtending 108deg and 36deg
4. The sum of the chords subtending 36deg and 36deg

Correct answer: The sum of the chords subtending 36deg and 60deg

Solution

Since chord = 2*R*sin(x/2), the claim reduces to sin(54deg) = sin(18deg) + sin(30deg); both sides equal about 0.809, so the 108deg chord equals the sum of the 36deg and 60deg chords.

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