Circles
NIOS · Class 10 · Maths
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A chord of length 16 cm is at a distance of 6 cm from the centre of a circle. What is the radius of the circle?
In a circle with centre O, if two chords AB and CD are equal, then which of the following is true?
The circumference of a circle is 44 cm. What is its radius? (Use π = 22/7)
A regular hexagon is inscribed in a circle. What angle does each side subtend at the centre?
Sample Questions
Two parallel chords of lengths 24 cm and 10 cm are on the same side of the centre. If the distance between them is 7 cm, what is the radius of the circle?
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13 cm
Step 1: Let distances from centre to chords be x and x+7. Let chord of 24 cm be at distance x, and 10 cm chord at distance x+7. Step 2: For 24 cm chord: r² = x² + 12² = x² + 144. Step 3: For 10 cm chord: r² = (x+7)² + 5² = (x+7)² + 25. Step 4: Equating: x² + 144 = (x+7)² + 25, so x² + 144 = x² + 14x + 49 + 25, giving 14x = 70, so x = 5. Step 5: Therefore, r² = 5² + 12² = 25 + 144 = 169, so r = 13 cm.
If the diameter of a circle is 28 cm, what is its area? (Use π = 22/7)
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616 cm²
Step 1: Given diameter = 28 cm, so radius = 28/2 = 14 cm. Step 2: Using the formula: Area = πr². Step 3: Substituting values: Area = (22/7) × 14². Step 4: Calculating: Area = (22/7) × 196 = 22 × 28 = 616. Step 5: Therefore, area = 616 cm².
In two concentric circles, the radius of the outer circle is 10 cm and inner circle is 6 cm. What is the area between the circles? (Use π = 22/7)
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176 cm²
Step 1: Area between circles = Area of outer circle - Area of inner circle. Step 2: Area of outer circle = π × 10² = (22/7) × 100 = 2200/7. Step 3: Area of inner circle = π × 6² = (22/7) × 36 = 792/7. Step 4: Area between = 2200/7 - 792/7 = (2200-792)/7 = 1408/7. Step 5: Therefore, area between = 1408/7 = 176 cm².
A chord subtends an angle of 120° at the centre of a circle of radius 12 cm. What is the length of the chord?
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12√3 cm
Step 1: Given central angle = 120° and radius = 12 cm. Step 2: For a chord subtending angle θ at centre: chord length = 2r sin(θ/2). Step 3: Here, θ/2 = 120°/2 = 60°. Step 4: Chord length = 2 × 12 × sin(60°) = 24 × (√3/2) = 12√3. Step 5: Therefore, chord length = 12√3 cm ≈ 20.8 cm.
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