Maths · Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre
Two parallel chords and are 3.9 cm apart and lie on opposite sides of the centre
Two parallel chords \( A B \) and \( C D \) are 3.9 cm apart and lie on opposite sides of the centre of a circle. If \( A B=1.4 \mathrm{cm} \) and \( C D=4 \mathrm{cm}, \) find the radius of the circle.
- A. \( 3 \mathrm{cm} \)
- B. \( 3.2 \mathrm{cm} \)
- C. 2 .3 \mathrm{cm} \)
- D. \( 2 \mathrm{cm} \)
Step-by-step solution
Let distances from centre to chords be d1 and d2. Since chords on opposite sides, d1 + d2 = 3.9 cm. For AB: r² = d1² + (0.7)², for CD: r² = d2² + 2². Equate: d1² - d2² = 3.51. Using d1 + d2 = 3.9, get d1 - d2 = 0.9, so d1 = 2.4, d2 = 1.5. Then r = sqrt(2.4² + 0.7²) = sqrt(6.25) = 2.5 cm. None of the given options are exactly 2.5, but the closest is C (2.3 cm); however, the correct radius is 2.5 cm.
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