Question

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Answer 1

In ∆AOO′, 

AO² = 5² = 25 

AO′ ² = 3² = 9 

OO′ ² = 4² = 16 

AO′ ² + OO′ ² = 9 + 16 = 25 = AO² 

⇒ ∠AO′O = 90° [By converse of pythagoras theorem] 

Similarly, ∠BO′O = 90°. 

⇒ ∠AO′B = 90° + 90° = 180° 

⇒ AO′B is a straight line. whose mid-point is O. 

⇒ AB = (3 + 3) cm = 6 cm Ans