O is the centre of a circle with diameter 20 cm. T is a point outside the circle and TA is a tangent to a circle. If OT is=26 cm, what is the length (in cm) of the tangent TA?

24

OT = 26 cm

Radius (OA) = \(\frac{20}{2}\) = 10 cm

OA is perpendicular to TA

So, \(\angle\)OAT = \({90}^\circ\)

In \(\Delta \)OAT, TA =√(\( {26 }^{2 } \) + \( { 10}^{2 } \))

⇒ √(676 - 100)

⇒ √576

⇒ 24 cm.

Therefore, the length of the tangent is 24 cm.