Circles

Answer

Step 1: Draw perpendicular from center O to chord AB. Let M be the foot of perpendicular. Step 2: OM = 3 cm (given distance) Step 3: AM = MB = 8/2 = 4 cm (perpendicular bisects chord) Step 4: In right…

Answer

Step 1: Let perpendicular distances from center be x and (x+1) Step 2: For 6 cm chord: r² = x² + 3² = x² + 9 Step 3: For 8 cm chord: r² = (x+1)² + 4² = (x+1)² + 16 Step 4: Since both equal r²: x² + 9 …

Answer

Step 1: Draw perpendicular OM from O to chord AB Step 2: In isosceles triangle AOB: ∠OAB = ∠OBA = (180° - 60°)/2 = 60° Step 3: Triangle AOB is equilateral (all angles 60°) Step 4: Therefore AB = OA = …

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Step 1: A regular hexagon has 6 equal sides Step 2: Central angle for each side = 360°/6 = 60° Step 3: Each side subtends 60° at center Step 4: Triangle formed by center and adjacent vertices is isosc…

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Step 1: Use area formula A = πr² Step 2: 154 = (22/7) × r² Step 3: r² = 154 × 7/22 = 1078/22 = 49 Step 4: r = √49 = 7 cm Step 5: Use circumference formula C = 2πr Step 6: C = 2 × (22/7) × 7 Step 7: C …

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Step 1: Let centers be O₁ and O₂ with radii r₁ = 5 cm, r₂ = 3 cm Step 2: Draw perpendicular from O₁ to PQ at M (midpoint) Step 3: PM = MQ = 6/2 = 3 cm Step 4: In right triangle O₁MP: O₁M² = O₁P² - PM²…

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Step 1: When two chords intersect inside a circle, we use the intersecting chords theorem Step 2: AP × PB = CP × PD Step 3: Substitute known values: 4 × 6 = 3 × PD Step 4: 24 = 3 × PD Step 5: PD = 24/…

Answer

Step 1: Area of minor segment = Area of sector - Area of triangle Step 2: Area of sector = (θ/360°) × πr² = (120°/360°) × π × 7² Step 3: Area of sector = (1/3) × (22/7) × 49 = 1078/21 cm² Step 4: For …