Two circles having diameter 10 cm and 24 cm. The distance between their centres is 13 cm. What is the length of their common chord (in cm)?

9.23

Diameters = 10 cm and 24 cm

So, radius = 5 cm and 12 cm

and distance b/w two centers = 13 cm

Therefore,

ΔAO₁O₂ having sides 5 cm, 12 cm, 13 cm is an right angle with ∠O₁AO₂ = 90º                            (5,12,13 ⇒ triplet)

In right angle triangle:

Length of perpendicular drawn on the hypotenuse from the right angle vertex (AC) = \(\frac{Perp. × base}{hypotenuse}\) = \(\frac{5 × 12}{13}\) = 4.615 cm

AB = 2 × AC = 2 × 4.615 = 9.23 cm