Question

the radii of two concentric circles are 40cm and 41cm. what is the length of a chord of the bigger circle which is tangent to the smaller circle​

Answer 1

{ Tangent is perpendicular to the radius at the point of contact }

Therefore, angle OAC is 90°

In ∆OAC,

• OA² = OC² + AC² { By Pythagoras theorem }
• AC = √OA² - OC²
• AC = √(41cm)² - (40cm)²
• AC = √1681 cm² - 1600 cm²
• AC = √81 cm²
• AC = 9 cm.

{ In two concentric circles the chord of the bigger circle that touches the smaller circle is bisected at the point of contact with the smaller circle }

Therefore, AB = 2 × AC = 2 × 9 cm = 18cm

Therefore, the length of the chord is 18cm

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