A chord of a circle is 10 cm long, and the radius of the circle is 13 cm. What is the perpendicular distance from the center of the circle to the chord?
Correct: D
When a radius (or part of it) is drawn perpendicular to a chord, it bisects the chord. This forms a right-angled triangle where:
- The hypotenuse is the radius (r = 13 cm).
- One leg is half the length of the chord (10 cm / 2 = 5 cm).
- The other leg is the perpendicular distance from the center to the chord (let's call it d).
Using the Pythagorean theorem: a^2 + b^2 = c^2
5^2 + d^2 = 13^2
25 + d^2 = 169
d^2 = 169 - 25
d^2 = 144
d = sqrt(144)
d = 12 cm.