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
Find the area of circle in sq. cms, in which the chord of length is at the dista
Find the area of circle in sq. cms, in which the chord of length \( 18 \mathrm{cm} \) is at the distance of half of the radius of circle from the centre of circle:
- A. \( 108 \pi \)
- B. \( 54 \pi \)
- C. \( 27 \pi \)
- D. \( 81 \pi \)
Step-by-step solution
Let radius be R. Distance from center to chord = R/2. Chord length = 2√(R² - (R/2)²) = 2√(R² - R²/4) = 2√(3R²/4) = R√3. Given chord = 18 cm, so R√3 = 18 → R = 18/√3 = 6√3 cm. Area = πR² = π(6√3)² = 108π cm².
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