MathematicsConsider a circle with center O and radius = 24cm. AB = 20cm and CD = 14cm are two chords of the circle. Which chord is farther away from the center?

Consider a circle with center O and radius = 24cm. AB = 20cm and CD = 14cm are two chords of the circle. Which chord is farther away from the center?

A
AB
B
CD
C
Both are equidistant from the center
D
None of these.

Solution:

Given,
Radius = 24cm.
AB = 20cm and CD = 14cm are two chords of the circle.
The length of a chord increases as the perpendicular distance from the center of the circle to the chord decreases and vice versa.
The diameter is the longest chord of a circle, where the perpendicular distance from the center of the circle to the diameter(longest) is zero.
Hence, CD is farther away from the centre.
Therefore, option 2 is correct.