NDA 2026 · PYQ · Trigonometry/Circle · medium
What is the length of the chord of a unit circle which subtends at the centre of the circle an angle of 45°?
- A.2√(2+√2) units
- B.2√(2-√2) units
- C.√(2+√2) units
- D.√(2-√2) units✓ Correct
Chord length = 2r sin(θ/2) = 2(1) sin(22.5°) = 2 sin 22.5°. sin 22.5° = √((1-cos 45°)/2) = √((1 - √2/2)/2) = √((2-√2)/4) = √(2-√2)/2. So chord = 2 · √(2-√2)/2 = √(2-√2) units.
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