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:
Answer & explanation
Correct answer: option 3
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.