What is the area of the region between two concentric circles, if the length of a chord of the outer circle touching the inner circle at a particular point of its circumference is 14 cm? (Take π = 22/7)
Answer
The correct answer is A: 154 square cm. The chord of the outer circle is tangent to the inner circle, so the perpendicular from the centre to the chord equals the inner radius r. Half-chord = 7 cm.
A.154 square cm✓ Correct
B.144 square cm
C.132 square cm
D.Cannot be determined due to insufficient data
Explanation
The chord of the outer circle is tangent to the inner circle, so the perpendicular from the centre to the chord equals the inner radius r. Half-chord = 7 cm. If R is the outer radius, then R² = r² + 7² = r² + 49. Area of annulus = π(R² - r²) = π × 49 = (22/7) × 49 = 154 sq cm.
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