The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

$5\sqrt{3}$ cm

Since XY is tangent

Therefore, Using Pythagoras theorem in OXY

\( {XO }^{2 } \) = \( {XY }^{2 } \) + \( {OY }^{2 } \)

\( {10 }^{2 } \) = \( {XY }^{2 } \) + \( {5 }^{2 } \)

100 = \( {XY }^{2 } \) + 25

75 = \( {XY }^{2 } \)

XY = 5\(\sqrt {3 }\) cm.

Therefore, the length of tangent is 5\(\sqrt {3 }\) cm.