In a circle of radius 13 cm, a chord is drawn at a perpendicular distance of 5 cm from the center. What is the length of the chord?
Answer and explanation
Correct answer: A. 24 cm
- Step 1: A line from center perpendicular to a chord bisects the chord. Step 2. In the right triangle formed: r² = d² + (0.5 L)² => 13² = 5² + (0.5 L)². Step 3. 169 = 25 + (0.5 L)² => (0.5 L)² = 144 => 0.5 L = 12 cm. Step 4. Total chord length L = 2 × 12 = 24 cm. Answer: 24 cm. Why not the others: 12 cm is the half-chord length; 20 cm and 18 cm result from non-Pythagorean errors.
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