In a circle, a ten cm long chord is at a distance of 12 cm from the centre of the circle. Length of the diameter of the circle (in cm) is:

26

In \(\Delta \)BDO,

BD = b = \(\frac{AB}{2}\) = \(\frac{10}{2}\) = 5 cm

PD = p = 12 cm

OB = h = Radius

Using pythagoras theorem

h = √ (\( {p }^{2 } \) + \( {b }^{2 } \))

= √ (\( {12 }^{2 } \) + \( {5 }^{2 } \))

= √(144 +25) = √169 = 13 cm.

Radius OB = 13 cm

Diameter = 2 x OB = 2 x 13 = 26 cm.

Therefore, length of diameter of the circle is 26 cm.