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Question:

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos⁻¹(1/7) and sec⁻¹(7) at the centre respectively, then the distance between these chords, is:

87

8√7

4√7

167

Solution:

cos²Q = 1/7
2cos²Q - 1 = 1/7
2cos²Q = 8/7
cos²Q = 4/7
cosQ = 2/√7
cp1 = 4√7
sec²Q = 7
1 + 2sin²Q = 7
2sin²Q = 6
sin²Q = 3
sinQ = √3
cp2 = 4√7
4√7 + 4√7 = 8√7