A chord of length 48 cm is drawn at a distance of 7 cm from centre of the circle. Calculate the radius of the circle.
Circles
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Question

A chord of length 48 cm is drawn at a distance of 7 cm from centre of the circle. Calculate the radius of the circle.

KnowledgeBoat · Accepted Answer

From figure,

AC is the chord and OB is the perpendicular distance of chord from the center.

Length of the chord AC = 48 cm.

B is the midpoint of AC, as OB is perpendicular to the chord AC.

AB = $\dfrac{1}{2}$ AC

= $\dfrac{1}{2} \times 48$

= 24 cm.

In Δ OAB, ∠B = 90°

Using Pythagoras theorem,

∴ OA² = OB² + AB²

⇒ OA² = (7)² + 24²

⇒ OA² = 49 + 576

⇒ OA² = 625

⇒ OA = $\sqrt{625}$ = 25 cm.

Hence, radius of circle is 25 cm.

Mathematics