Calculate the length of a chord which is at a distance 12 cm from the centre of a circle of radius 13 cm.
Circles
177 Likes

Question

Calculate the length of a chord which is at a distance 12 cm from the centre of a circle of radius 13 cm.

KnowledgeBoat · Accepted Answer

From figure, AB is the chord which is at a distance 12 cm so, OC = 12 cm and OA = radius = 13 cm. In right angle triangle OAC, ⇒ OA² = OC² + AC² (By pythagoras theorem) ⇒ 13² = 12² + AC² ⇒ AC² = 13² - 12² ⇒ AC² = 169 - 144 = 25 ⇒ AC = = 5 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ CB = AC = 5 cm. AB = AC + CB = 5 + 5 = 10 cm. Hence, length of chord = 10 cm.

Mathematics

Calculate the length of a chord which is at a distance 12 cm from the centre of a circle of radius 13 cm.

Circles

Related Questions

A chord of length 48 cm is drawn in a circle of radius 25 cm. Calculate its distance from the centre of the circle.

A chord of length 8 cm is at a distance 3 cm from the centre of the circle. Calculate the radius of the circle.

Calculate the length of a chord which is at a distance 6 cm from the center of a circle of diameter 20 cm.

A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.