What is the diameter of the circle?
Consider the following for the next two (02) items that follow : Two parallel chords AB and CD of a circle are of lengths 60 cm and 80 cm respectively. They are on the same side of the centre O and 10 cm apart.
- A. 120 cm
- B. 110 cm
- C. 100 cm ✓
- D. 90 cm
Correct Answer: C. 100 cm
Explanation
Let x be the distance from the center to CD. Using Pythagoras theorem for both chords: r^2 = x^2 + 40^2 and r^2 = (x+10)^2 + 30^2. Equating them yields x^2 + 1600 = x^2 + 20x + 1000, so 20x = 600 \implies x = 30. Then r^2 = 30^2 + 40^2 = 2500 \implies r = 50. The diameter is 100 cm.
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