In a circle, the length of a chord is 30cm. The perpendicular distance of the chord from the centre of the circle is 8 cm. Find the diameter of the circle.

34 cm

Let AB be the chord and O be the center of the circle.

Also, OP is perpendicular to AB

In \(\Delta \)OPB,

\( {OB }^{2 } \) = \( {PB }^{2 } \) + \( {OP }^{2 } \)

\( {OB }^{2 } \) = \( {15 }^{2 } \) + \( {8 }^{2 } \)

\( {OB }^{2 } \) = 225 + 64

OB = 17

Diameter = 2 x OB = 2 x 17 = 34

Therefore, the diameter of the circle is 34 cm.