Question

The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is = ___ cm.

Answer 1

$\angle$ABO= ${90}^{\circ }$ (point of contact)

Using Pythagoras theorem

${AO}^2$= ${AB}^2$+ ${BO}^2$

${25}^2$= ${AB}^2$+ $7^2$

${25}^2$ - $7^2$ = ${AB}^2$

24= AB

length of the tangent = 24 cm