Circle

Answer

Step 1: Half of the chord = 6/2 = 3 cm. Step 2: Use OA² = OP² + AP². Step 3: 5² = OP² + 3². Step 4: 25 = OP² + 9. Step 5: OP² = 16, so OP = 4 cm. Answer: The distance from the centre is 4 cm.

Answer

Step 1: Half of the chord = 8/2 = 4 cm. Step 2: Use OA² = OP² + AP². Step 3: OA² = 3² + 4². Step 4: OA² = 9 + 16 = 25. Step 5: OA = 5 cm. Answer: The radius is 5 cm.

Answer

Step 1: Let half the chord be x cm. Step 2: Use OA² = OP² + AP². Step 3: 17² = 8² + x². Step 4: 289 = 64 + x². Step 5: x² = 225, so x = 15 cm. Step 6: Full chord = 2 × 15 = 30 cm. Answer: The chord is…

Answer

Step 1: Half the chord = 24/2 = 12 cm. Step 2: Use OA² = OP² + AP². Step 3: r² = 5² + 12². Step 4: r² = 25 + 144 = 169. Step 5: r = 13 cm. Answer: The radius is 13 cm.

Answer

Step 1: From the first chord, half-length = 12 cm. Step 2: Radius = 13 cm from OA² = OP² + AP². Step 3: For the second chord, let half-length be x cm. Step 4: Use 13² = 12² + x². Step 5: 169 = 144 + x…

Answer

Step 1: For the 30 cm chord, half-length = 15 cm. Step 2: Distance from centre = √(17² - 15²) = √(289 - 225) = √64 = 8 cm. Step 3: For the 16 cm chord, half-length = 8 cm. Step 4: Distance from centre…

Answer

Step 1: Distance of the 30 cm chord from centre = 8 cm. Step 2: Distance of the 16 cm chord from centre = 15 cm. Step 3: On the same side, distance between chords = 15 - 8 = 7 cm. Answer: The distance…

Answer

Take the two triangles formed by joining the centre to the two ends of the chord and to its midpoint. Step 1: The two radii are equal. Step 2: The two halves of the chord are equal. Step 3: The shared…