A chord is 5 cm from the center of a circle of radius 13 cm. The length of the chord is?
- 30 cm
- 5 cm
- 24 cm
- None of these
Explanation
Given:
Radius (r) = 13 cm
Distance from center to chord (d) = 5 cm
Let's draw a perpendicular from the center to the chord. This will bisect the chord.
Using the Pythagorean theorem:
r² = d² + (half chord)²
13² = 5² + (half chord)²
169 = 25 + (half chord)²
(half chord)² = 169 - 25
= 144
half chord = √144
= 12 cm
Length of chord = 2 × half chord
= 2 × 12
= 24 cm
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