Question

from a point Q length of the tangent to a circle is 24cm and the tangent of a Q from the centre is 25cm, The radius of a circle is??​

Answer 1

Let O be the centre of a circle ,from an external

point Q ( such that OQ =25 cm. ) a tangent ( QP

=24 cm ) is drawn. Join O to P. OP is the radius of the circle. Angle OPQ =90°.

In right angled triangle OPQ

OP^2+PQ^2=OP^2

r^2+24^2=25^2

r^2 =625–576= 49

r =7 cm. ,

Answer 2

A tangent is perpendicular to the radius through the point of contact.Using Pythagoras theorem, in ∆OTQ,we have

$\longrightarrow$$\large\tt\red{ {OT}^{2} = {OQ}^{2} - {QT}^{2} }$

$\longrightarrow$$\large\tt\purple{{(25)}^{2} - {(24)}^{2} }$

$\longrightarrow$$\large\tt\green{625-576}$

$\longrightarrow$$\large\tt\blue{49}$

$\large\sf\pink{Hence,the\:option(A)\:is\:correct}$