Question

choose the correct option and give justification.
from a point $Q$, the length of the tangent to a circle is 24 cm and the distance of $Q$ from the centre is $25cm$. The radius of the circle is

• A. $7cm$
• B. $12cm$
• C. $15cm$
• D. $24.5cm$

Answer 1

The correct option is A $7cm$

Tangent $=XY$

Let point of contact be ${}^{\prime }{B}^{\prime }$

length of the tangent to a circle $=24cm$

i.e., $PQ=24cm$

& $OQ=25c,$

$\because XY$ is tangent, $OP\perp XY$

so, $\angle OPQ={90}^o$

so, $△OPQ$ is a right angled triangle

Using phythagoras therom

$(x{)}^2=(P{)}^2+(B{)}^2$

$(25{)}^2=(QP{)}^2+(24{)}^2$

$(OP{)}^2=(25{)}^2+(24{)}^2$

$(OP{)}^2=625-576$

$(OP{)}^2=49$

$OP=\sqrt{(7{)}^2}=OP=7$

radius $OP=7cm$

Option $A$ is correct