Multiple choice

Two equal chords of two circles make angles (60^{\circ}) and (75^{\circ}). Then the ratio of the radii of the circles is?

  1. 5 : 2

  2. 5 : 4

  3. 3 : 2

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal chords of lengths c in circles with radii r1 and r2, making angles θ1 and θ2: c = 2r1sin(θ1/2) = 2r2sin(θ2/2). Therefore r1/r2 = sin(θ2/2)/sin(θ1/2) = sin(75°/2)/sin(60°/2) = sin(37.5°)/sin(30°) = sin(37.5°)/(1/2) = 2sin(37.5°). Using sin(37.5°) = sin(75°/2) and the half-angle formula, sin(37.5°) ≈ 0.608, giving ratio ≈ 1.216, or 5:4.

Keep practicing — related questions