Question

If radius of circle is 13 cm, and length of its one chord is 10 cm, then find the length of the chord from the center.

Answer 1

Let O is the center of given circle and radius is 13 cm, chord AB = 10 cm

OM ⊥ AB.

We know that perpendicular drawn from center bisect the chord.

Thus AM = MB

∵ AB = 10 cm

then AM = MB = \(\frac { 1 }{ 2 }\) × AB

= \(\frac { 1 }{ 2 }\) × 10 = 5 cm

In right angled ΔOMA in which ∠M is right angle,

By Pythagoras theorem

OA² = OM² + AM²

⇒ (13)² = (OM)² + (5)²

⇒ 169 = OM² + 25

⇒ OM² = 169 – 25

⇒ OM² = 144

⇒ OM = \(\sqrt { 144 }\)

⇒ OM= 12 cm

Thus, distance of chord AB from center is 12 cm