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Two parallel chords of a circle of radius R lie on the same side of the centre and subtend angles of 72deg and 144deg respectively at the centre. What is the perpendicular distance between the two chords?
- R/2
- R
- R/4
- R*sqrt(2)/2
Correct answer: R/2
Solution
The chord distances from the centre are R*cos 36deg and R*cos 72deg; their difference cos 36deg - cos 72deg = 1/2, so the gap is R/2.
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