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.
Answer & explanation
Correct answer: option 4
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.