PX is a tangent drawn from point X, touches the circle at P, O is the centre of the circle. Radius of this circle is 10 cm and OX = 26 cm. What is the length of PX ?

24 cm

Here PX is the tangent makes 90 degrees angle with the radius.

In triangle OPX,

OP = 10 cm

OX = 26 cm

Apply Pythagoras theorem

\( { OX}^{2} \) = \( {OP }^{2 } \) + \( {PX }^{ 2} \)

= \( { 26}^{2} \) = \( {10 }^{2 } \) + \( {PX }^{ 2} \)

= \( {PX }^{ 2} \) = 676 - 100

= \( {PX }^{ 2} \) = 576

= PX = 24 cm

Therefore, PX is 24 cm.