Mathematics

The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the centers.

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Let AB be the chord of the circle with center O. Draw OC ⊥ AB.

We know that,

Perpendicular from the center of circle to the chord, bisects the chord.

∴ AC = $\dfrac{AB}{2} = \dfrac{24}{2}$ = 12 cm.

In right-angled triangle OAC,

⇒ OA² = OC² + AC²

⇒ 13² = OC² + 12²

⇒ 169 = OC² + 144

⇒ OC² = 169 - 144

⇒ OC² = 25

⇒ OC = $\sqrt{25}$ = 5 cm.

Hence, the distance of the chord from the center = 5 cm.

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